Question

√(x+√(x+11)) + √(x-√(x+11))=4

Answer 1

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