how to solve eqn (120/x)^2+(x/2)^2=13^2

Question

can we solve

Answer 1

Expand: 14400/x^2+x^2/4=169.

Multiply through by 4x^2:

57600+x^4=676x^2.

x^4-676x^2+57600=0=(x^2-100)(x^2-576)

x^2=100 or 576. So x=±10 or ±24. Four solutions: x=-24, -10, 10, 24.

CHECK

±120/24=±5; ±24/2=±12 so 25+144=169=13^2 OK

±120/10=±12; ±10/2=±5 so 144+25=13^2 OK