Question

If [x^(1/3)] - [x^(1/9)] = 60 then find the value of x

Answer 1

Answer:

The value of x=262144.

Step-by-step explanation:

Given : $x^{\frac{1}{3}}-x^{\frac{1}{9}}=60$

To find : The value of x?

Solution :

$x^{\frac{1}{3}}-x^{\frac{1}{9}}=60$

Taking $x^{\frac{1}{9}}$ common

$x^{\frac{1}{9}}(x^{\frac{2}{9}}-1)=60$

Taking $x^{\frac{1}{9}}=y$

$y(y^2-1)=60$

By hit n trial the value of y=4

As it satisfy the equation,

$4(4^2-1)=60$

$4(15)=60$

$60=60$

Now, $x^{\frac{1}{9}}=4$

Taking log both side,

$\log (x^{\frac{1}{9}})=\log (4)$

$\frac{1}{9}\log (x)=\log (4)$

$\log (x)=9\log (4)$

$\log (x)=\log (4)^9$

$x=4^9$

$x=262144$

Therefore, The value of x=262144.