Math, asked by Shooter3413X, 1 month ago

Pls Help Me I Will Give Extra Points If You Give Correct Answer

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Answered by CopyThat
88

Answer:

a = 8

b = 3

Step-by-step explanation:

\bold{\dfrac{3+\sqrt{7} }{3-\sqrt{7} } =a+b\sqrt{7} }

Rationalizing denominator:

\bold{\dfrac{3+\sqrt{7} }{3-\sqrt{7} }\times\dfrac{3+\sqrt{7} }{3+\sqrt{7} }  }

\bold{\dfrac{(3+\sqrt{7})^2 }{(3)^2-(\sqrt{7})^2 } }

Since:

  • (a + b) × (a + b) = (a + b)²
  • (a - b) × (a + b) = a² - b²
  • (a + b)² = a² + b² + 2ab

\bold{\dfrac{9+6\sqrt{7}+7 }{9-7} }

\bold{\dfrac{16+6\sqrt{7} }{2} }

Taking 2 common:

\bold{\dfrac{2(8+3\sqrt{7}) }{2} }

Cancelling 2:

\bold{8+3\sqrt{7}=a+b\sqrt{7}  }

∴ a = 8 & b = 3.

Answered by rahulas703
2

it will help you, thanks

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