Question 446023
{{{(x^2-1)^(1/2)+1/(x^2-1)^(1/2)=5/2}}},multiply both sides by {{{(x^2-1)^(1/2)}}}

{{{(x^2-1)+1=(5/2)(x^2-1)^(1/2)}}}=>{{{x^2=(5/2)(x^2-1)^(1/2)}}}. Raise to the

second power both sides of equation:{{{x^4=(25/4)(x^2-1)}}}, set the equation to 

zero:{{{4x^4-25x^2+25=0}}}, substitute {{{x^2=y}}} and get a quadratic equation:

{{{4y^2-25y+25=0}}}, solving this equation we find:y=5 and y=5/4.

Knowing that, {{{x^2=5}}}, get {{{x=sqrt(5)}}} and {{{x=-sqrt(5)}}}

Also from {{{x^2=5/4}}}, we get {{{x=sqrt((5)/2)}}} and {{{x=-sqrt((5)/2)}}}

Thus, the solution set is:[ {{{sqrt(5)}}}, {{{-sqrt(5)}}}, {{{sqrt(5)/2}}}, 

{{{-sqrt(5)/2}}}]