Minimum value of $frac{b+1}{a+b-2}$
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If $a^2 + b^2= 1 $ and $u$ is the minimum value of the $dfrac{b+1}{a+b-2}$, then find the value of $u^2$. Attempt: Then I tried this way: Let $a= bk$ for some real $k$. Then I got $f(b)$ in terms of b and k which is minmum when $b = dfrac{2-k}{2(k+1)}$ ... then again I got an equation in $k$ which didn't simplify. Please suggest an efficient way to solve it.
calculus derivatives trigonometry optimization quadratics
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edited Jan 2 at 11:42
greedoid
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