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Question
The sum of two numbers is 7 and the sum of their cubes is 133, find the sum of their square.
Solution
Let a, b be the two numbers.
.'. a + b = 7 and a3 + b3 = 133
(a + b)3 = a3 + b3 + 3ab (a + b)
⇒ (7)3 = 133 + 3ab (7)
⇒ 343 = 133 + 21ab
⇒ 21ab = 343 - 133 = 210
⇒ 21ab = 210
⇒ ab= 10
Now a2 + b2 = (a + b)2 - 2ab
= 72 - 2 x 10 = 49 - 20 = 29
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