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Question -

If a + b = 10 and ab = 21, find the value of a3 + b3.



Answer -

a + b = 10, ab = 21
Cubing both sides,
(a + b)3 = (10)3
⇒ a3 +63 + 3ab (a + b) = 1000
⇒ a3 + b3 + 3 x 21 x 10 = 1000
⇒ a3 + b3 + 630 = 1000
⇒ a3 + b3 = 1000 – 630 = 370
∴ a3 +b3 = 370

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