Question

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

Answer 1

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.

Answer 2

it will help you, thanks