Answer:
Step-by-step explanation:
[tex]\frac{10}{\sqrt{2}+\sqrt{7}}=\frac{10*(\sqrt{2}-\sqrt{7})}{(\sqrt{2}+\sqrt{7})*(\sqrt{2}-\sqrt{7})}\\\\=\frac{10*(\sqrt{2}-\sqrt{7})}{(\sqrt{2})^{2}-(\sqrt{7})^{2}}\\\\=\frac{10*(\sqrt{2}-\sqrt{7})}{2-7}\\\\=\frac{10*(\sqrt{2}-\sqrt{7})}{-5}\\\\=-2*(\sqrt{2}-\sqrt{7})\\\\= -2\sqrt{2}+2\sqrt{7}[/tex]
Hint: (a + b)(a -b)= a² - b²
(√2+√7)(√2-√7)=(√2)²-(√7²) = 2 - 7 = -5
