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Question

If a + b = 10 and ab = 16, find the value of a2ab+b2 and a2+ab+b2.

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Solution

a + b = 10, ab = 16

Squaring,

(a+b)2=(10)2 a2+b2+2ab=100 a2+b2+2×16=100 a2+b2+32=100 a2+b2=10032=68Now, a2ab+b2=a2+b2ab=6816=52and a2+ab+b2=a2+b2+ab=68+16=84


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