Mathematics, 15.07.2020 02:01 sarabell7626
If (ax+b)(bx+a)=26x^2+ Box(x) +26, where a, b, and Box are distinct integers, what is the minimum possible value of Box, the coefficient of x?
Answers: 2
![\frac{d}{da} (\frac{a^3+26}{a})=\frac{2a^3-26}{a^2}\\$Setting the derivative equal to zero, we have:\\2a^3-26=0\\2a^3=26\\a^3=13\\a=\sqrt[3]{13}](/tpl/images/0706/7086/1a5ee.png)
![\Box=a^2+b^2=\dfrac{(\sqrt[3]{13}) ^3+26}{\sqrt[3]{13}}\\=\dfrac{13+26}{\sqrt[3]{13}}\\\\\Box=16.59](/tpl/images/0706/7086/3b2ee.png)
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If (ax+b)(bx+a)=26x^2+ Box(x) +26, where a, b, and Box are distinct integers, what is the minimum po...
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