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Question: If x = a + b, y = aw + bw<sup>2</sup> and z = aw<sup>2</sup> + bw then which one of the following is...

If x = a + b, y = aw + bw2 and z = aw2 + bw then which one of the following is true –

A

x3 + y3 + z3 = 3 (a3 + b3)

B

xyz = 2 (a3 + b3)

C

x + y + z ¹ 0

D

x2 + y2 + z2 = a2 + b2

Answer

x3 + y3 + z3 = 3 (a3 + b3)

Explanation

Solution

Sol. Y\overset{̶}{Z} = a2 + b2 – ab \ XY\overset{̶}{Z} = a3 + b3 X

& X +Y + \overset{̶}{Z} = 0 X

& X2 + Y2 + {\overset{̶}{Z}}^{2}

= a2 + b2 +2ab + a2w2 +b2w+ 2ab + a2w4 + b2w2 + 2ab

= 6ab X