a, b and c are integers, la-bl to the power of 19 + lc-al to the power of 99=1, what is the value of lc-al +la-bl + lb-cl?
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a + b = 8, ab = 6
Cubing both sides,
(a + b)3 = (8)3
⇒ a3 + b3 + 3 ab{a + b) = 512
⇒ a3 + b3 + 3 x 6 x 8 = 512
⇒ a3 + b3 + 144 = 512
⇒ a3 + b3 = 512 – 144 = 368
∴ a3 + b3 = 368
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