Question

Find the value of x3 + y3 + z3

– 3xyz, if x + y + z = 12 and x

2 + y2 + z2 =70
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Answer 1

Answer:

Step-by-step explanation:

x + y + z = 12 and x² + y² + z² = 70

(x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx

= (12)² = 70 + 2 (xy + yz + zx)

= 2 (xy + yz + zx) = 144 - 70 = 74

xy + yz + zx=74/2

= xy + yz + zx = 37

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

= (12) (70-37) = 12 x 33 = 396

So the value of x³ + y³ + z³ - 3xyz is 396

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