Question

find the value of x cube + y cube + Z cube minus 3 x y z if X square + Y square + Z square is equal to 83 and X + Y + Z is equal to 15​

Answer 1

Given:

x²+y²+z²=83

x+y+z=15

To find:

x³+y³+z³-3xyz

Solution:

1) by the formulas of the algebra we have

x³+y³+z³-3xyz = (x+y+z)(x²+y²+z²-xy-yz-xz)

2) So we need to find the value of the xy+yz+xz

3) Square the term x+y+z=15 we get

• x²+y²+z²+2xy+2yz+2xz = 225

• 2(xy+yz+xz) = 225-83

• 2(xy+yz+xz) = 142

• (xy+yz+xz) = 71

4) Putting the value of the term in the equation we get

• x³+y³+z³-3xyz = (x+y+z)(x²+y²+z²-xy-yz-xz)

• x³+y³+z³-3xyz = (15)(83-71)

x³+y³+z³-3xyz = 180

Answer 2

Step-by-step explanation:

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