Question

(2- (sq root 5))/(2+3(sq root 5))=(a (sq root 5) + b) pls tell me answer for a and b ..rationalise denominator 9 class cbse number systems

Answer 1

Hey friend,
Here is the answer you were looking for:
$\frac{2 - \sqrt{5} }{2 + 3 \sqrt{5} } = a \sqrt{5} + b \\ \\ on \: rationalizing \: the \: denominator \: we \: get \\ \\ = \frac{2 - \sqrt{5} }{2 + 3 \sqrt{5} } \times \frac{2 - 3 \sqrt{5} }{2 - 3 \sqrt{5} } \\ \\ using \: the \: identity \\ (a + b)(a - b) = {a}^{2} - {b}^{2} \\ \\ = \frac{2 \times 2 - 2 \times 3 \sqrt{5} - \sqrt{5} \times 2 + \sqrt{5} \times 3 \sqrt{5} }{ {(2)}^{2} - {(3 \sqrt{5}) }^{2} } \\ \\ = \frac{ 4 - 6 \sqrt{5} - 2 \sqrt{5} + 15 }{4 - 45} \\ \\ = \frac{19 - 8 \sqrt{5} }{41} \\ \\ \frac{ - 8 \sqrt{5} + 19}{41} = a \sqrt{5} + b \\ \\ a = \frac{ - 8}{41} \\ \\ b = \frac{19}{41}$

Hope this helps!!!

@Mahak24

Thanks...
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