Question

5^3/4 = 4√x then 3√x = ?

pls answer my question fast​

Answer 1

By trial, x=2 is a root of the equation . Dividing the equation by 5x we get 

(53)x+(54)x=1

If x<2, then (3/5)x>(3/5)2

and (4/5)x>(4/5)2  and so on 

(3/5)x+(4/5)x>(3/5)2+(4/5)2=1

Hence (1) is not satisfied for any value of x<2.

Similarly, for x>2, we will always have the inequality (3/5)x+(4/5)x<1

Thus x=2 is the only root of the given equation. Note that it is immaterial how we found a root, but it is necessary to show that there are no other roots.