Question
Solve the equations involving square roots
\sqrt{x+5}+\sqrt{20-x} =7
Solve the equations involving square roots
\sqrt{x+5}+\sqrt{20-x} =7
\sqrt{x+5}+\sqrt{20-x} =7
Square both sides of the equation,
x+5+2\sqrt{x+5}\sqrt{20-x}+20-x=49
\sqrt{x+5}\sqrt{20-x}=12
Square both sides of the equation again,
(x+5)(20-x) = 144
x^2-15x+44=0
Factoring the quadratic expression on left hand side
(x-4)(x-11)=0
Now we have found the solution for the equation.
x=4 or x=11