Question

√(x+√(x+11)) + √(x-√(x+11))=4

Answer 1

$sqrt{x+ sqrt{x+11}}+sqrt{x- sqrt{x+11}}=4 \ \ (sqrt{x+ sqrt{x+11}}+sqrt{x- sqrt{x+11}} )^2=4^2 \ \ x+ sqrt{x+11}+ 2*sqrt{x+ sqrt{x+11}}*sqrt{x- sqrt{x+11}} +x- sqrt{x+11}=16 \ \ 2x+ 2*sqrt{(x+ sqrt{x+11})*(x- sqrt{x+11})}=16 \ \ 2x+ 2*sqrt{x^2 - (x+11)}=16 \ \ x+sqrt{x^2 -x-11)}=8 \ \ sqrt{x^2 -x-11)}=8-x \ \ (sqrt{x^2 -x-11)})^2=(8-x)^2 \ \ x^2 -x-11=64-16x+ x^{2} \ \ 15x=75 \ \ x=5$