If x + y = 12 and xy = 14 then find the value of (x2 + y2).

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Solution

using the identity (a+b)2=a2+b2+2ab
(x+y)2=x2+y2+2xy
(12)2=x2+y2+2(14)
144=x2+y2+28
144-28=x2+y2
116=x2+y2
therefore x2+y2=116

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