Question 839982
A rectangle with an area of 60 square feet has a diagonal of 13 feet. find the sides of the rectangle.

this is for roots but we can use any method ancient or modern.

I know xy=60 and x^2 + y^2=13^2
--------------
y = 60/x
{{{x^2 + (60/x)^2 = 169}}}
{{{x^2 + 3600/x^2 = 169}}}
{{{x^4 + 3600 = 169x^2}}}
{{{x^4 - 169x^2 + 3600 = 0}}}
Sub u for x^2
{{{u^2 - 169u + 3600 = 0}}}
*[invoke solve_quadratic_equation 1,-169,3600]
=====================
{{{y^2 = 144}}}
x = 12
y = 5
or vice versa