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X^2+y^2+z^2-xy-yz-zx formula-X 2 y 2 z 2 xy yz zx = 2 (x 2 y 2 z 2 xy yz zx) = 2x 2 2y 2 2z 2 2xy 2yz 2zx = x 2 x 2 y 2 y 2 z 2 z 2 2xy 2yz 2zx Since square of any number is positive, the given equation is always positive Is there an error in this question or solution?If x y z = 6 and xy yz zx = 10, then the value of x3 y3 z3 3xyz is?
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It's true for 15!If x y = 4, xy = 2, y z = 5, yz = 3, z x = 6 and zx = 4 Formula used x 3 y 3 z 3 3xyz = (x y z) × (x 2 y 2 z 2 – xy – yz – zx) (x y) 2 = x 2 y 2 2xy Calculations x y = 4, y z = 5, z x = 6 So, x y z = 15/2 = 75 xy yz zx = 2 3 4 = 9 Now, (x y) 2 = x 2 y 2 2xy x 2 y 2 = 16 – 4 (2xy = 4)X^2y^2z^2xyyzzx= {(xy)^2}{(yz)^2}{(zx)^2}÷2 sum of squares of three real nos is zero if each is equal to zero so, xy=0, yz=0, zx=0 therefore, x=y=z
X^2y^2z^2xyyzzx=0 multiplying the RHS and LHS by 2 we get , 2 x^2y^2z^2xyyzzx =0 or, (xy)^2(yz)^2(zx)^2=0 since in LHS there are only squared terms,ie they cannot be negative What are factors of 4x^212xy9y^24x6y35?The formula of x 3 y 3 z 3 – 3xyz is written as \(\begin{array}{l}x^{3} y^{3} z^{3} – 3xyz = (x y z) (x^{2} y^{2} z^{2} – xy – yz – zx)\end{array} \) Let us prove the equation by putting the values of x = 1; Ex 42, 9 By using properties of determinants, show that 8 (x&x2&yz@y&y2&zx@z&z2&xy) = (x – y) (y – z) (z – x) (xy yz zx) Solving LHS 8 (𝑥&𝑥^2&𝑦𝑧@𝑦&𝑦^2&𝑧𝑥@𝑧&𝑧^2&𝑥𝑦) Applying R1→ R1 – R2 = 8 (𝑥−𝑦&𝑥^2−𝑦^2&𝑦𝑧−𝑥𝑧@𝑦&𝑦^2&𝑧𝑥@𝑧&𝑧^2&𝑥𝑦) Ex 42, 9 By using properties of determinants, show that 8 (x&x2&yz@y&y2&zx@z&z2&xy) = (x – y) (y – z) (z –
M4maths Previous Puzzles Which one statement is correct If x2 y2 z2 xy yz zx 0 then which one statement is correct OPtion 1) x = y = z 2) x > y > z 3) x y z 4) x ≠ y = z 5) x = y ≠ z 6) x ≠ y ≠ zBecause if x = y = z, then x * y = x^2 = y^2, xz = x^2 = z^2, and yz = y^2 = z^2!We compute X Y, Y Z, Z X XY, YZ, ZX X Y, Y Z, ZX using the distance formula Step 3 3 of 7 29 < 41 ⇒ X Y 2 Y Z 2 < Z X 2 29
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If x y z = 10, x3 y3 z3 = 75 and xyz = 15, then find the value of x2 y2 z2 – xy – yz – zx 1 3 2 5 3 6 4 4The three loci of double points x = 0, y = 0, and z = 0, intersect at a triple point at the origin For example, given x = yz and y = zx, the second paraboloid is equivalent to x = y/z Then = and either y = 0 or z 2 = 1 so that z = ±1 Their two external intersections are x = y, z = 1;SolutionShow Solution x y z = 4 and x 2 y 2 z 2 = 30 Since ( x y z)2 = x2 y2 z2 2 ( xy yz zx ), we have (4)2 = 30 2 ( xy yz zx ) ⇒ 16 = 30 2 ( xy yz zx ) ⇒ 2 ( xy yz zx ) = 14 ⇒ xy yz zx = 14 2 = 7 ∴ xy yz zx = 7 Concept Expansion of Formula
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X^2y^2z^2=1 WolframAlpha Area of a circle? x y z = 5 x 2 y 2 z 2 = 21 y 2 = zx x 2 y 2 z 2 – xy – yz – zx = 1212 (x – y) 2 (y – z) 2 (z – x) 2 Solved examples using AB Whole Cube formula Now you can understand this (AB) 3 formula in detail by solving some good examples
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Algebra Examples Rewrite (xy z)2 ( x y z) 2 as (xyz)(xyz) ( x y z) ( x y z) Expand (xyz)(xyz) ( x y z) ( x y z) by multiplying each term in the first expression by each term in the second expression Simplify each term Tap for more steps Multiply x x by x x Multiply y y by y yLearn about Algebra Formula, Equations and List of Basic Algebraic Formulas & Expression in Math Algebra includes real numbers, complex numbers, matrices, vectors and many other topics x 2 y 2 z 2 −xy−yz−zx=1/2(x−y) 2 (y−z) 2 (z−x) 2 If n is a natural number,The value of x y z if x2 y2 z2 18 and xy yz zx 9 is a 9 b 3 c 6 d 8 Hint – In this question use the direct algebraic identity that ${\left( {x y z} \right)^2} = {x^2} {y^2} {z^2} 2\left( {xy yz zx} \right)$, substitution of the given values will help evaluating the value of x y z
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Find stepbystep Physics solutions and your answer to the following textbook question Calculate the divergence of the following vector functions $$ \vec{v}_a=x^2 x2y2z2=xyyzzx you can get 2x22y22z2=2xy2yz2zx which equals 2x22y22z22xy2yz2zx=0,the equivalant is (xy)2(yz)2(zx)2=0Easy as pi (e) Unlock StepbyStep Natural Language Math Input Use Math Input Mode to directly enter textbook math notation
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পণ্যটি সন্ধান করুন।(xyz)(x^2y^2z^2xyyzzx) পণ্যটি সন্ধান করুন।(xyz)(x^2y^2z^2xyyzzx) Books Physics NCERT DC Pandey Sunil Batra HC Verma Pradeep Errorless Areas of Parallelograms and Triangles Circles Coordinate Geometry Herons Formula Introduction to EuclidsHere we are going to see some example problems based on the formula x 3 y 3 z 3 3xyz = (x y z)(x 2 y 2 z 2 xy yz zx) X cube plus Y cube plus Z cube minus 3xyzFactor x^2y^2 x2 − y2 x 2 y 2 Since both terms are perfect squares, factor using the difference of squares formula, a2 −b2 = (ab)(a−b) a 2 b 2 = ( a b) ( a
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Let us consider LHS of the equation LHS = x 3 y 3 z 3 – 3xyz LHS = 1 3 2 3 3 3 – 3Formula of polynomials If the polynomial k 2 x 3 − kx 2 3kx k is exactly divisible by (x3) then theShow that `(x,x^(2),yz),(y,y^(2),zx),(z,z^(2),xy)=(xy)(yz)(zx)(xyyzzx)` Very Important Questions Using Ampere 's circuital law or Biot Savart's a law, show that magnetic flux density B at point P at a perpendicular distance a from a long current carrying conductor is given by
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If x y z = 8 and xy yz zx = find the value of x3 y3 z3 3xyz ClassIX Maths Polynomials Meghna deshnur What must be subtracted from 4x^42x^36x^22x6 so that the result is exactly divisible by 2x^2x1? with $\alpha=x$ , $\beta=y$ , $\gamma=z \quad\to\quad =\frac{xdxydyzdz}{(xz^22xyzxy^2) (xy^2xyz)(xyzxz^2)}= \frac{xdxydyzdz}{0}$ This implies $xdxydyzdz=0 \quad\implies\quad x^2y^2z^2=c_1$Extended Keyboard Examples Upload Random Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music
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Anything subtracted from zero gives its negation xyxzxyz=yz x y x z − x y z = − y z Combine all terms containing x Combine all terms containing x \left (yzyz\right)x=yz ( y z − y z) x = − y z The equation is in standard form The equation is in standard form Despite the fact that the same variables appear in every term, this expression does not factorize into one term There is no common factor, and no common bracket EAch term can be factored by differemce of squares xy(x^2y^2) yz(y^2z^2) zx(z^2x^2) =xy(xy)(xy) yz(yz)(yz) zx(zx)(zx) The only other option would be to multiply out the brackets and tryA) 36 b) 40 c) 42 d) 48
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02 x m / x n = x mn;03 (xy) m = x m × y m;X^3y^3z^33xyz= (xyz) (x^2y^2z^2xyyzzx)/a^3b^3c^33abc= (abc) (a^2b^2c^2abbcca) x^3y^3z^33xyz= (xyz) (x^2y^2z^2xyyzzx)/a^3b^3c^33abc= (abc) (a^2b^2c^2
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Show that log (x^2/yz) log(y^2/zx) log (z^2/xy) = 0 Question Show that Formula's Used Solution LHS We know that Now use property log a log b = log ab{x}^{2}{y}^{2}{z}^{2}xyyzzx=0 Rightarrow;2{x}^{2}2{y}^{2}2{z}^{2}=2xy2yz2zx=0 Rightarrow left({x}^{2}{y}^{2}2xyright)left({y}^{2}{z}^{2}2yzright)left({zX 2 y 2 z 2 2xy 2yz 2zx = 4 ⇒ x 2 y 2 z 2 = 4 – 2 × (11) = 26 Putting the values in the given formula we get, ⇒ 2 × 26 – (11) ⇒ 2 × 37 ⇒ 74
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Square Formula 01 (xy) 2 06 x 3 – y 3 = (x – y)(x 2 xy y 2) 07 (x y) 4 = x 4 4x 3 y 6x 2 Advertisement y 2 4xy 3 y 4) (x – y) 10 x 3 y 3 z 3 – 3xyz = (x y z)( x 2 y 2 z 2 xy – yz – zx) Laws of Exponent 01 x m × x n = x mn;Now, (x^2 y^2 z^2) = (x y z)^2 2 * (xy yz zx) Or, (x^2 y^2 z^2) = (u^2 2v) So, w = u * (u^2 2v v) = u * (u^2 3v) Or, w = u^3 3 * u * v We know, that any three functions f, g and h are said to be in linear combinations if any relationship exists between them like If x y z = 12, x2 y2 z2 = 64 , find the value of xy yz zx Maths Polynomials
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Ex 25, 12 Verify that x3 y3 z3 – 3xyz = 1/2 (x y z)(x – y)2 (y – z)2 (z – x)2 Solving RHS 1/2 (x y z)(x – y)2 (y – z)2 (z – x Important Statistics Formulas (I) The Mean of Grouped Data can be found by 3 methods Direct Method formula This method can be very calculation intensive if the values of f and x are largeWe have big calculations and chance of making mistake is quite high 2 Assumed mean method formula Where a= Assumed mean and d i = x i –a This method is quite useful(xyz)^3 (x y z)(x y z)(x y z) We multiply using the FOIL Method x * x = x^2 x * y = xy x * z = xz y * x = xy y * y = y^2
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A Not Quite Cyclic Inequality from Tibet $\left((xy)^2(z^2xzx^2xyy^2yz)^2\ge 8(xyyzzx)^2(x^2y^2)\right)$ An inequality in 22 variables from SSMA magazine $\left(\displaystyle k^2\tan\alphal^2\tan\beta\ge\frac{2kl}{\sin (\alpha\beta)}(k^2l^2)\cot(\alpha\beta)\right)$4 4 4 4 4 4 = 0, and 2 = 2 = 2!225 225 225 225 225 225 = 0, and 15 = 15 = 15!
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x^2y^2z^2=xyyzzx (1) multiplying by (xyz) on both sidesx^2y^2z^2 (xyz)=(xyyzzx ) (xyz) expand the above equationsx^3y^3z^3xy^2x^2 yyz^2y^2 zxz^2x^2 z=x^2 yxyzzx^2xy^2 y^2 zxyzxyz yz^2 xz^2 simplifying x^3y^3z^3=3xyz04 (x m) n = x mn;One The number one Or if both are true, any number!
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