SOLUTION: sqrt(x^2-2)/sqrt(7 x-25)= sqrt(2) I need help its me for Find all real solutions of the equation. (If there are extra answer boxes, enter NONE in the last boxes.) ive tried every

Algebra ->  Radicals -> SOLUTION: sqrt(x^2-2)/sqrt(7 x-25)= sqrt(2) I need help its me for Find all real solutions of the equation. (If there are extra answer boxes, enter NONE in the last boxes.) ive tried every      Log On


   

Question 321244: sqrt(x^2-2)/sqrt(7 x-25)= sqrt(2)
I need help its me for Find all real solutions of the equation. (If there are extra answer boxes, enter NONE in the last boxes.) ive tried everything but i still do not understand can you send me how you guys performed this operation i'd appreciate it thanks
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28x%5E2-2%29%2Fsqrt%287x-25%29= sqrt%282%29
this can be written under a single radical on the left
sqrt%28%28x%5E2-2%29%2F%287x-25%29%29= sqrt%282%29
Now we have a single radical on each side, square both sides and we're rid of em
%28x%5E2-2%29%2F%287x-25%29 = 2
Multiply both sides by (7x-25), and you have
:
x^2 - 2 = 2(7x - 25)
:
x^2 - 2 = 14x - 50
arrange as a quadratic equation on the left
x^2 - 14x - 2 + 50 = 0
:
x^2 - 14x + 48 = 0
Easily factors to
(x-8)(x-6) = 0
Two solutions
x = 8
and
x = 6
:
Check both these solutions in the original problem using a calc
x=8
sqrt%288%5E2-2%29%2Fsqrt%287%288%29-25%29= sqrt%282%29
sqrt%2862%29%2Fsqrt%2831%29= 1.414
7.874%2F5.568= 1.414; confirms this solution
:
You should check x=6, the same way