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

Total Price: Rs.

There are no items in this cart.
Continue Shopping
akhil mahajan Grade: 12

Find the no. of values of x belongs to R for which

64^(1/x) + 48^(1/x) = 80^(1/x)

plzz give the full soln...

7 years ago

Answers : (3)

mycroft holmes
271 Points

Let 1/x = y.


The equation then becomes . Divide by 8y on both sides to obtain 


. If y<0, then there are no solutions.


LHS is a strictly monotonic function in y. Hence there can exist at most one solution to the equation. y = 2 is a solution and hence the unique solution. (You can also use the Power Mean Inequality to arrive at this conclusion)


Hence x = 1/2 is the only solution.

7 years ago
Vihit Khanna
31 Points


  (64)^1/x +(48)^1/x=(80)^1/x

=>Tahe 16^1/x common on both side s.t.

(16X4)^1/x +  (16X3)^1/x =(16X5)^1/x

=>4^1/x + 3^1/x=5^1/x

=>By pythgerous triplet

 4^2 + 3^2=5^2



7 years ago
akhil mahajan
36 Points

e1 i got the same answer


but the answer given is that there r 4 solutions!!!!

7 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. 150 off
USE CODE: Test150
Get extra Rs. 150 off
USE CODE: Test150

Ask Experts

Have any Question? Ask Experts

Post Question

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