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If a+b=1,a >0, prove that (a+1/a)^2+(b+1...

If `a+b=1,a >0,` prove that `(a+1/a)^2+(b+1/b)^2geq(25)/2dot`

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To prove that \( (a + \frac{1}{a})^2 + (b + \frac{1}{b})^2 \geq \frac{25}{2} \) given that \( a + b = 1 \) and \( a > 0 \), we will follow these steps: ### Step 1: Rewrite the Expression We start with the expression we need to prove: \[ (a + \frac{1}{a})^2 + (b + \frac{1}{b})^2 \] ...
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