Q10 of 90 Page 33

Verify that:

x3 + y3 + z3 – 3xyz = 1/2 (x + y + z)[(x – y)2 + (y – z)2 + (z – x)2]

Taking R.H.S





= x3 + x2y + xz2 – x2y – xyz – zx2 + x2y + y3 + z2y – xy2 – y2z – xyz + x2z + y2z + z3 – xyz – yz2 – z2x)


= x3 + y3 z3 – 3xyz


(other terms got cancelled)


= L.H.S


More from this chapter

All 90 →
8

Factorize :

125x3 – 64y3 – 300x2y + 240xy2

 9

Factorize:

(i) 64a3 + 27b3


(ii) 125x3 – 8y3

 10

Verify that:

27a3 + b3 + c3 – 9abc = (3a + b + c)[3a2 + b2 + c2 – 3ab – bc – 3ac]

 11

If x + y + z = 0 then verify that x3 + y3 + z3 = 3xyz.