# Solve 7^x + 343/7^x = 56

How to find the value of *x*.

I couldn't go after this:

7^{x} + $\frac{343}{7^x}$ = 56

Pls help, the 7^{x} is confusing.

Go to main content# Solve 7^x + 343/7^x = 56

How to find the value of *x*.

I couldn't go after this:

7^{x} + $\frac{343}{7^x}$ = 56

Pls help, the 7^{x} is confusing.

You just need to replace the 7^{x} with something like *k* or *a*. This makes urs simplification method much more easier.

So the solution is:

7^{x} + $\frac{343}{7^x}$ = 56

let 7^{x} = k

so, k + $\frac{343}{k}$ = 56

or, k^{2} - 56k + 343

or, k^{2} - (7 + 49)k + 343 = 0

or, k^{2} - 7x - 49k + 343 = 0

or, k(k - 7) - 49(k - 7) = 0

or, (k - 7)(k - 49) = 0

Either, k = 7

so, 7^{x} = 7^{1}

so, x = 1

OR, k = 49

so, 7^{x} = 7^{2}

so, x = 2

Hence, x = 1, 2

Video explanation: