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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 squares.

A
30
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B
41
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C
29
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D
49
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Solution

The correct option is C 29

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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