hoaton7ovy4od
hoaton7ovy4od hoaton7ovy4od
  • 04-06-2020
  • Mathematics
contestada

Simplify the expression.

[tex]\frac{10}{\sqrt{2}+\sqrt{7} }[/tex]

Respuesta :

devishri1977
devishri1977 devishri1977
  • 10-06-2020

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

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