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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.

Answers(3)

Answer

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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