If a + b = 10 and ab = 16, find the value of a² + b².
68
Using the identity \((a+b)^2 = a^2+b^2+2ab\), we get \(a^2+b^2 = (a+b)^2-2ab\).
Substituting the given values: \(a^2+b^2 = 10^2 - 2(16) = 100-32\).
Therefore, \(a^2+b^2 = 68\).
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