Question

I was doing calc hw and I am stuck on a part of a question.

=(1/10)-(x/15sqrt(x^2-9))

I am supposed to put this equation equal to 0 and solve for x.
The answer is 9/sqrt(5) but I don't understand how the answer comes out to be 9/sqrt(5). Please help. Thank you.

Answer 1

(1/10)-(x/15sqrt(x^2-9))=0
(1/10)=(x/15sqrt(x^2-9))
Cross multiply:
15√(x²-9)=10x
3√(x²-9)=2x
Square both sides
9(x²-9)=4x²
9x²-81=4x²
5x²=81
x²=(81/5)
take square-root
x=9/sqrt(5)