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Let A = x y z y z x z x y , where x , y and z are real numbers such that x + y + z > 0 and x y z = 2 . If A 2 = I 3 , then the value of x 3 + y 3 + z 3 is

Correct answer

0

Step-by-step solution

A 2 = I ⇒ A A ' = I (as A ' = A ) ⇒ A is orthogonal So, x 2 + y 2 + z 2 = 1 and x y + y z + z x = 0 ⇒ x + y + z 2 = 1 + 2 × 0 ⇒ x + y + z = 1 Thus, x 3 + y 3 + z 3 = 3 × 2 + 1 × 1 - 0 =   7

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