Math, asked by Diva11th, 1 year ago

find the value of a and b

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Answered by DaIncredible
2
Hey friend,
Here is the answer you were looking for:
 \frac{3 +  \sqrt{7} }{3 -  \sqrt{7} }  = a + b \sqrt{7}  \\

On rationalizing the denominator we get,

 =  \frac{3 +  \sqrt{7} }{3 -  \sqrt{7} }  \times  \frac{3 +  \sqrt{7} }{3 +  \sqrt{7} }  \\

Using the identities:
 {(a + b) }^{2}  =  {a}^{2}  +  {b}^{2}   + 2ab \\ (a + b)(a - b) =  {a}^{2}  -  {b}^{2}

Putting a = 3
and b = √7

 =  \frac{ {(3)}^{2} +   {( \sqrt{7} )}^{2}  + 2(3)( \sqrt{7}) }{(3)^{2}  - ( \sqrt{7})^{2}  }  \\  \\  =  \frac{9 + 7 + 6 \sqrt{7} }{9 - 7}  \\  \\  =  \frac{16 + 6 \sqrt{7} }{2}  \\  \\  =  \frac{2(8 + 3 \sqrt{7}) }{2}  \\  \\  = 8 + 3 \sqrt{7}  \\  \\ 8 +  3\sqrt{7}  = a + b \sqrt{7}  \\  \\ a = 8 \:  : b = 3

Hope this helps!!

If you have any doubt regarding to my answer, feel free to ask in the comment section or inbox me if needed.

@Mahak24

Thanks...
☺☺
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