SOLUTION: Solve the following equation: (18/x)^2+x^2=45. Show your work.

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Question 957570: Solve the following equation:
(18/x)^2+x^2=45. Show your work.
Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
(18/x)^2+x^2=45
324%2Fx%5E2+%2B+x%5E2+-+45+=+0
324+%2B+x%5E4+-+45x%5E2+=+0
x%5E4+-+45x%5E2+%2B+324+=+0
%28x%5E2-9%29%2A%28x%5E2-36%29+=+0
x = -3,3,-6,6

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
%2818%2Fx%29%5E2%2Bx%5E2=45
324%2Fx%5E2%2Bx%5E2=45.....both sides multiply by x%5E2
324x%5E2%2Fx%5E2%2Bx%5E2%2Ax%5E2=45x%5E2
324%2Bx%5E4=45x%5E2
x%5E4-45x%5E2%2B324=0............replace -45x%5E2 with -9x%5E2-36x%5E2
x%5E4-9x%5E2-36x%5E2%2B324=0 .........group
%28x%5E4-9x%5E2%29-%2836x%5E2-324%29=0............factor out x%5E2from first group and 36 from second group
x%5E2%28x%5E2-9%29-36%28x%5E2-9%29=0
%28x%5E2-36%29%28x%5E2-9%29=0
%28x%5E2-6%5E2%29%28x%5E2-3%5E2%29=0..........factor, use difference of squares rule
%28x-6%29%28x%2B6%29%28x-3%29%28x%2B3%29+=0
solutions:
x=6
x=-6
x=3
x=-3

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+150%2C+%2818%2Fx%29%5E2%2Bx%5E2-45%29+