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Example 6. On what basis can we say that we should take (x+y)²???
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We know the value of x+y and also of xy. We have to find x^2+y^2. If you think, squarring both sides will give you (x+y)^2 which will be x^2+y^2+2xy. You can use this to find x^2+y^2. It's a bit of intuition.
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It's just a way by using an identity.... Such questions are designed to be solved by using identities...
Given:
x+y = 12
xy = 32
(x+y)² = x² + y² + 2xy
=> (12)² = x² + y² + 2(32)
=> 144 = x² + y² + 64
=> 144 - 64 = x² + y²
=> x² + y² = 80.
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