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Question
If a − b = 5 and ab = 12, find the value of a2 + b2
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Solution
We have to find the value `a^2 +b^2`
Given a-b = 5, ab = 12
Using identity `(a - b)^2 = a^2 - 2ab +b^2`
By substituting the value of a-b = 5 ,ab = 12 we get ,
`(5)^2 = a^2 +b^2 - 2 xx 12`
`5 xx 5 = a^2 +b^2 - 2 xx 12`
`25 = a^2 +b^2 -24`
By transposing – 24 to left hand side we get
`25 + 24 = a^2 +b^2`
`49 = a^2 +b^2`
Hence the value of `a^2 +b^2` is 49.
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