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Meghna deshnur

Jul 26, 2013

# If x + y + z = 8 and xy + yz + zx = 20 find the value of x3 + y3 + z3 - 3xyz.

If x + y + z = 8 and xy + yz + zx = 20 find the value of x3 + y3 + z3 - 3xyz.

Kishore Kumar

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 = 82 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

Chundi Sasidhar kumar reddy

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 = 82 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

Syeda

Answer. 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 = 82 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
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