if X +y+Z =10, xy+yz+ zx=-15 and xyz=-12 then find the value of x^2+y^2+z^2 and x^3+y^3+z^3
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Given x + y + z = 8 and xy + yz + zx = 20
Consider, x + y + z = 8 Squaring on both sides,
we get (x + y + z)2 = 8^2
x2 + y2 + z2 +2(xy + yz +zx) = 64
⇒ x2 + y2 + z2 = 64 − 2(xy + yz +zx)
= 64 − 2(20) = 64 − 40 = 24
∴ x2 + y2 + z2 = 24
We know that
x3 + y3 + z3 − 3xyz = (x + y + z)( x2 + y2 + z2 − xy − yz − zx)
= 8(24 −20)
= 8(4)
= 32
Plz mark my answer brainliest
Consider, x + y + z = 8 Squaring on both sides,
we get (x + y + z)2 = 8^2
x2 + y2 + z2 +2(xy + yz +zx) = 64
⇒ x2 + y2 + z2 = 64 − 2(xy + yz +zx)
= 64 − 2(20) = 64 − 40 = 24
∴ x2 + y2 + z2 = 24
We know that
x3 + y3 + z3 − 3xyz = (x + y + z)( x2 + y2 + z2 − xy − yz − zx)
= 8(24 −20)
= 8(4)
= 32
Plz mark my answer brainliest
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