Question

Решите пожалуйста: √(8+2√(10+2√5))+√(8-2√(10+2√5))

Answer 1

$\sqrt{8+2\sqrt{10+2\sqrt{5}}}+\sqrt{8-2\sqrt{10+2\sqrt{5}}}=n\\\bigstar \ \ \left ( a+b \right )^2=a^2+2ab+b^2\\8+2\sqrt{10+2\sqrt{5}}+8-2\sqrt{10+2\sqrt{5}}+2\sqrt{24-8\sqrt{5}}=n^2\\n^2=16+2\sqrt{24-8\sqrt{5}}=16+2\left ( 2\sqrt{5}-2 \right )=12+4\sqrt{5}\\n=\sqrt{12+4\sqrt{5}}$