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If x + y + z = 10 x3 + y3...

This question belongs to Arithmetic Ability Algebra
Algebra
?

If x + y + z = 10, x3 + y3 + z3 = 75 and xyz = 15, then find the value of x2 + y2 + z2 - xy - yz - zx.

Answer & Solution
Correct Answer: Option B
x3 + y3 + z3 = (x + y + z)(x2 + y2 + z2 - xy - yz - zx)
75 - 3 × 15 = 10(x2 + y2 + z2 - xy - yz - zx)
x2 + y2 + z2 - xy - yz - zx = 3
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