Question
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