Question 957570
{{{(18/x)^2+x^2=45}}}

{{{324/x^2+x^2=45}}}.....both sides multiply by {{{x^2}}}

{{{324x^2/x^2+x^2*x^2=45x^2}}}

{{{324+x^4=45x^2}}}

{{{x^4-45x^2+324=0}}}............replace {{{-45x^2}}} with {{{-9x^2-36x^2}}}

{{{x^4-9x^2-36x^2+324=0}}} .........group

{{{(x^4-9x^2)-(36x^2-324)=0}}}............factor out  {{{x^2}}}from first group and  {{{36}}} from second group

{{{x^2(x^2-9)-36(x^2-9)=0}}}

{{{(x^2-36)(x^2-9)=0}}}

{{{(x^2-6^2)(x^2-3^2)=0}}}..........factor, use difference of squares rule

{{{(x-6)(x+6)(x-3)(x+3) =0}}}

solutions:

{{{x=6}}}
{{{x=-6}}}
{{{x=3}}}
{{{x=-3}}}


{{{ graph( 600, 600, -10, 10, -10, 150, (18/x)^2+x^2-45) }}}