Question

If x+y+z=0 show that x³+y³+z³=2xyz using it find the value of (17)³-(5)³-(12)³

Answer 1

Step-by-step explanation:

Given

x+y+z=0

solution-

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

x³+y³+z³-3xyz=0(x²+y²+z²-xy-yz-zx)

anything multiplied by 0 is 0

x³+y³+z³-3xyz=0

x³+y³+z³=3xyz

hence proved

the value of (17)³-(5)³-(12)³

let's check if a+b+c=0

17+(-5)+(-12)

17-5-12

17-17

0

so,if a+b+c=0 then x³+y³+z³=3xyz

=3*17*5*12

=3060

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