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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...

6 years ago

Answers : (3)

mycroft holmes
266 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.

6 years ago
Vihit Khanna
31 Points
										

Given:


  (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


=>1/x=2


=>x=1/2=0.5

6 years ago
akhil mahajan
36 Points
										

e1 i got the same answer


 


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

6 years ago
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