MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
Menu
aritra nandy Grade: 10
        

if y=x+1/y prove that (x2-y2+3)dy/dx=1

6 years ago

Answers : (2)

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 question
Difficult 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 Experts
Priyansh Bajaj

6 years ago
vikas askiitian expert
510 Points
										

x=y-1/y ...........1


differentiating wrt x


 1 = dy/dx -1/y2 (dy/dx)


dy/dx=y2 /1+y2  ................2


we have to prove (x2 -y2 +3 )dy/dx =1       or


                      x2 -y2 +3 =1/(dy/dx)


taking LHS


                    = (x-y)(x+y)+3                     (putting x from eq 1)


                   = y2 +1/y2  .....................4


taking RHS


                     =1/(dy/dx)=(y2+1)/y2 .............5


FROM 4 & 5


LHS = RHS


hence proved


 

6 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies
  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: Rs. 15,900
  • View Details
Get extra Rs. 3,180 off
USE CODE: CART20
Get extra Rs. 339 off
USE CODE: CART20

Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details