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aritra nandy Grade: 10
```        if y=x+1/y
prove that (x^2-y^2+3)dy/dx=1

need the answer fast urgent.```
6 years ago

## Answers : (1)

Priyansh Bajaj AskiitiansExpert-IITD
30 Points
```										Dear Aritra,
Solution:-  y = x +1/y.................(1)
dy/dx = 1 - (1/y2) (dy/dx)
[1 + (1/y2)] (dy/dx) = 1..................(2)
From eq. (1), y-1/y = x. On squaring both sides, we get-
(y-1/y )2= x2 or  y2 + 1/y2 -2= x2 or 1/y2 = (x2 - y2+2)
Putting the value of 1/y2  in eq. (2), we get-
[1 + (x2 - y2+2)] (dy/dx) = 1
(x2 - y2+3) (dy/dx) = 1
Hence proved.
Please feel free to post as many doubts on our discussion forum as you can. If you find any questionDifficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation.
All the best Aritra!!!
Regards,Askiitians ExpertsPriyansh Bajaj
```
6 years ago
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