Question

solve this im sharing picture

Answer 1

x + y +z = 0

=> x + y = - z ----------(1)

On cubing both sides, we get

x^3 + y^3 + 3xy ( x +y) = - z^3

=> x^3 + y^3 + 3xy ( - z) = - z^3 [ using equation 1]

=> x^3 + y^3 - 3xyz = - z^3

=> x^3 + y^3 + z^3 = 3xyz


Now,


( - 12) + 7 + 5 = - 12 + 12 = 0

So,

(-12)^3 + 7^3 + 5^3 = 3 (-12)(7)(5)

= - 1260

Answer 2

x + y +z = 0

=> x + y = - z ----------(1)

On cubing both sides, we get

x^3 + y^3 + 3xy ( x +y) = - z^3

=> x^3 + y^3 + 3xy ( - z) = - z^3 [ using equation 1]

=> x^3 + y^3 - 3xyz = - z^3

=> x^3 + y^3 + z^3 = 3xyz

Now,

( - 12) + 7 + 5 = - 12 + 12 = 0

So,

(-12)^3 + 7^3 + 5^3 = 3 (-12)(7)(5)

= - 1260

hope it helped ⚡