Question

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

Answer 1

Answer:

The answer is:   'no solution'

Step-by-step explanation:

The given equation is:   $3\sqrt{5x-4}=3\sqrt{7x+8}$

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

$\sqrt{5x-4}=\sqrt{7x+8}$

Taking square on both sides.....

$(\sqrt{5x-4})^2=(\sqrt{7x+8})^2\\ \\ 5x-4=7x+8\\ \\ 5x-7x=8+4\\ \\ -2x=12\\ \\ x=\frac{12}{-2}=-6$

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

$3\sqrt{5(-6)-4}=3\sqrt{7(-6)+8}\\ \\ 3\sqrt{-34}=3\sqrt{-34}$

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.

Answer 2

X = -6

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