Question

if x+y+z=9 and x2 + y2 +z2 + 35 find the value of x3 + y3 +z3 - 3xyz

Answer 1

x+y+z=9
x²+y²+z²=35. (x+y+z)²=x²+y²+z²+2xy+2zx+2yz
or 9²= 35+2(xy+yz+zx)
or 81-35 = 2(xy+yz+zx)
or 46/2 = xy+yz+zx
or -23 = -xy-yz-zx
So,x³+y³+z³-3xyz
=(x+y+z)(x²+y²+z²-xy-yz-zx
=9*(35-23)
=9*12
=108

Answer 2

Answer:

The final answer for the following equation is 108.

Step-by-step explanation:

we need to solve the equation given by substituting the values given and find the appropriate answer by substitution and using the principles of multiplication.

$x+y+z=9$

$x^2+y^2+z^2=35$

We need to find the value of

$x^3+y^3+z^3+3xyz$

by using the above information.

First we need to remember the rule,

$(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ac$

So by applying our equation in the above rule we get,

$(x+y+z)^2=x^2+y^2+z^2+2xy+2xz+2yz$

We know that,

$x+y+z=9$

and

$x^2+y^2+z^2=35$

$(9)^2 = 35 - 2xy+2xz+2yz$

$81 = 35 +2xy+2yz+2xz$

$81-35=2(xy+xz+yz)$

$46/2=(xy+yz+xz)$

$xy+xz+yz=23$

$-xy -xz-yz=$$-23$

$x^3+y^3+z^3 -3xyz=$$(x+y+z)(x^2+y^2+z^2-xy-yz-xz)$

$x^3+y^3+z^3 -3xyz=$$(9)(35-23)$

$x^3+y^3+z^3 -3xyz=$$9 * 12$

$x^3+y^3+z^3 -3xyz= 108$

The final answer we get by substituting and solving the equations is 108.

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