Question Number 142218 by Dwaipayan Shikari last updated on 27/May/21
![Straight line lx+my=1 is tangent to the curve (ax)^n +(by)^n =1 Prove that ((l/a))^(n/(nā1)) +((m/b))^(n/(nā1)) =1](https://www.tinkutara.com/question/Q142218.png)
$${Straight}\:{line}\:{lx}+{my}=\mathrm{1}\:\:{is}\:{tangent}\:{to}\:{the}\:{curve}\:\left({ax}\right)^{{n}} +\left({by}\right)^{{n}} =\mathrm{1} \\ $$$${Prove}\:{that}\:\left(\frac{{l}}{{a}}\right)^{\frac{{n}}{{n}ā\mathrm{1}}} +\left(\frac{{m}}{{b}}\right)^{\frac{{n}}{{n}ā\mathrm{1}}} =\mathrm{1} \\ $$
Answered by som(math1967) last updated on 28/May/21
![](https://www.tinkutara.com/question/20696.png)
Commented by Dwaipayan Shikari last updated on 28/May/21
![Thanks sir ! I have done this in a same way](https://www.tinkutara.com/question/Q142237.png)
$${Thanks}\:{sir}\:!\:{I}\:{have}\:{done}\:{this}\:{in}\:{a}\:{same}\:{way} \\ $$