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`        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

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.
```
7 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
```
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
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