Question

koi nahi bata raha 18sep ko exam hai pls bata do 3rd baar pooch raha hoon
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Answer 1

$\underline{ \huge\bf\red{QuestiØn} :}$

Given :-

$\boxed{ \frac{7 + 3 \sqrt{5} }{3 + \sqrt{5} } = a + b \sqrt{5} }$

Find :-

• a

• b

$\underline{ \: \huge\bf\green{SolutiØn} \: :}$

We have,

$\begin{aligned} \\ &\qquad \frac{7 + 3 \sqrt{5} }{3 + \sqrt{5} } \\ \\ & = \frac{7 + 3 \sqrt{5} }{3 + \sqrt{5} } \times \frac{3 - \sqrt{5} }{3 - \sqrt{5} } \\ \\ & = \frac{(7 + 3 \sqrt{5})(3 - \sqrt{5} ) }{(3 + \sqrt{5})(3 - \sqrt{5} ) } \\ \\ & = \frac{7(3) + 7( - \sqrt{5} ) + 3 \sqrt{5}(3) + 3 \sqrt{5}( - \sqrt{5}) }{ {(3)}^{2} - {( \sqrt{5} )}^{2} } \\ \\ & = \frac{21 - 7 \sqrt{5} + 9 \sqrt{5} - 15 }{9 - 5} \\ \\ & = \frac{6 + 2 \sqrt{5} }{4} \\ \\ & = \frac{3}{2} + \frac{1}{2} \sqrt{5} \end{aligned}$

Thus,

$\dfrac{3}{2} + \dfrac{1}{2} \sqrt{5} \ = \ a + b \sqrt{5}$

On comparing both the sides, we get :-

• $a = \dfrac{3}{2}$

• $b = \dfrac{1}{2}$

$\red{\rule{5.8cm}{0.02cm}}$

$\mid \underline{\underline{\LARGE\bf\green{Brainliest \: Answer}}}\mid$