Question

What is the solution to the equation 3sqrt(5x-4)=3sqrt(7x+8)

Answer 1

x = -6

However this is an extraneous solution since it would make the number under the sqrt a negative number.

Answer 2

The answer is: 'no solution'

Explanation:

The given equation is:
`3√(5x-4)=3√(7x+8)`

Dividing both sides of the equation by 3, we will get.....

`√(5x-4)=√(7x+8)`

Taking square on both sides.....

`(√(5x-4))^2=(√(7x+8))^2\\ \\ 5x-4=7x+8\\ \\ 5x-7x=8+4\\ \\ -2x=12\\ \\ x=(12)/(-2)=-6`

Plugging this
`x=-6` back to the given equation......

`3√(5(-6)-4)=3√(7(-6)+8)\\ \\ 3√(-34)=3√(-34)`

As we are getting a negative number inside the square root, so the equation becomes imaginary. Thus
`x=-6` is a restricted value.

Hence, there is 'no solution' for this equation.