If x=332, y=333, z=335, then the value of x^{ | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The algebraic identity for $x^{3}+y^{3}+z^{3}-3xyz$ is given by:$x^{3}+y^{3}+z^{3}-3xyz = \frac{1}{2}(x+y+z)[(x-y)^{2}+(y-z)^{2}+(z-x)^{2}]$Given

Vedclass · Accepted Answer

$7000$

Vedclass · Answer

(A) The algebraic identity for $x^{3}+y^{3}+z^{3}-3xyz$ is given by:$x^{3}+y^{3}+z^{3}-3xyz = \frac{1}{2}(x+y+z)[(x-y)^{2}+(y-z)^{2}+(z-x)^{2}]$Given $x=332, y=333, z=335$.First,calculate the sum: $x+y+z = 332+333+335 = 1000$.Next,calculate the differences:$(x-y) = 332-333 = -1 \implies (x-y)^{2} = 1$$(y-z) = 333-335 = -2 \implies (y-z)^{2} = 4$$(z-x) = 335-332 = 3 \implies (z-x)^{2} = 9$Now,substitute these values into the identity:$= \frac{1}{2} 	imes 1000 	imes (1 + 4 + 9)$$= 500 	imes 14$$= 7000$

If $x=332, y=333, z=335,$ then the value of $x^{3}+y^{3}+z^{3}-3xyz$ is

Similar Questions

The value of $c$ for which $|{\alpha ^2} - {\beta ^2}| = \frac{7}{4}$,where $\alpha$ and $\beta$ are the roots of $2{x^2} + 7x + c = 0$,is

If the sum of the roots of a quadratic equation is $1$ and the product of the roots is $-20$, find the quadratic equation.

If ${x^{2/3}} - 7{x^{1/3}} + 10 = 0,$ then $x = $

Solve the given two equations and select the correct option.
$I.$ $x = (1331)^{1/3}$
$II.$ $2y^2 - 17y + 36 = 0$

If $\alpha$ and $\beta$ are the roots of $x^2 - ax + b = 0$ and if $\alpha^n + \beta^n = V_n$,then -

Vedclass Test Series

Exam Paper Generator

Online Exam Module