Question

Найди значение выражения x2 + 2x√7 + 11, если x = √7 + 1.

Answer 1

$\displaystyle\bf\\x=\sqrt{7} +1\\\\\\x^{2} +2x\sqrt{7} +11=(\sqrt{7} +1)^{2} +2\sqrt{7} \cdot(\sqrt{7} +1)+11=\\\\\\=(\sqrt{7})^{2} +2\cdot \sqrt{7} \cdot 1+1^{2} +2\sqrt{7} \cdot \sqrt{7} +2\sqrt{7} \cdot 1+11=\\\\\\=7+2\sqrt{7} +1+2\cdot 7+2\sqrt{7} +11=4\sqrt{7} +33$