# 161 - Mathematics Questions Answers

$If\frac{9}{a}+\frac{24}{b}=1,a,b,\beta \x88\x88{\mathrm{\beta \x84\x9d}}^{+},provethat{a}^{2}+{b}^{2}\beta \x89\u20af9{(4+\sqrt[3]{9})}^{3}.$

**Asked By: JAMES GHOSH**

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**Asked By: PREM**

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**Joshi sir comment**

If a,b and c are positive real numbers, show that

$\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\beta \x89\u20af\frac{3}{2}$

**Asked By: MROY**

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**Asked By: LUFFY**

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$Letthelinesinthepairare{m}_{1}x-y=0and{m}_{2}x-y=0\phantom{\rule{0ex}{0ex}}Findperpendicularsfrom({x}^{,},{y}^{,})onlinesandcalculatetheirsum\phantom{\rule{0ex}{0ex}}Useformulae{m}_{1}+{m}_{2}=-\frac{2h}{b}and{m}_{1}{m}_{2}=\frac{a}{b}\phantom{\rule{0ex}{0ex}}$Inform for any issue

**Asked By: LUFFY**

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**Joshi sir comment**

length for one turn = 3

Draw diagonal of a rectangle then turn it as a cylinder, you will get the construction given in the question.

$Intrianglel=\sqrt{{3}^{2}+{n}^{2}}\phantom{\rule{0ex}{0ex}}Sototallengthofwirehavingnturn=n\sqrt{{3}^{2}+{n}^{2}}\phantom{\rule{0ex}{0ex}}Comparewith20andsolve$

**Asked By: KANDUKURI ASHISH**

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**Joshi sir comment**

$Thegeneralsolutionofthiskindof\phantom{\rule{0ex}{0ex}}differentialeq.isy={e}^{ax}\phantom{\rule{0ex}{0ex}}Letafunctiong\left(x\right)={e}^{ax}f\left(x\right)\left(1\right)\phantom{\rule{0ex}{0ex}}differentiateeq.\left(1\right)thriceforgetting{g}^{,,,}\left(x\right)\phantom{\rule{0ex}{0ex}}nowforgettingthesamefunctionasgiven\phantom{\rule{0ex}{0ex}}finda.yougetthesamefunctionfor\phantom{\rule{0ex}{0ex}}a=1/2.clearly,formin5zerosofg\left(x\right),\phantom{\rule{0ex}{0ex}}therearemin2zerosfor{g}^{,,,}\left(x\right).\phantom{\rule{0ex}{0ex}}solveandinformiffaceanyproblem.$