Question

15a^2+4b^2/15a^2-4b^2 = 47/7

find a/b

Answer 1

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

= 15²+4²+2(15)(3)(15+3)
----------------------------
15²-4²-2(15)(3)(15-3)
= 225+16+90x18
------------------------
225-16-90x18
= 47/7

Answer 2

Hello friend

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✍✍✍✍.

$\frac{(15a {}^{2} + 4b {}^{2}) }{(15a {}^{2} - 4b {}^{2}) } = \frac{47}{7} \\ \\ \frac{(15a {}^{2} + 4b {}^{2} ) + (15a {}^{2} - 4b {}^{2} )}{(15a {}^{2} + 4b {}^{2} ) - (15a {}^{2} - 4b {}^{2}) } = \frac{47 + 7}{47 - 7} ........(componendo - dividendo) \\ \\ \frac{15a {}^{2} + 4b {}^{2} + 15a {}^{2} - 4b {}^{2} }{15a {}^{2} + 4b {}^{2} - 15a {}^{2} + 4b {}^{2} } = \frac{54}{40} \\ \\ \frac{30a {}^{2} }{8b {}^{2} } = \frac{54}{40} \\ \\ \frac{a {}^{2} }{b {}^{2} } = \frac{54 \times 8}{40 \times 30} \\ \\ \frac{a {}^{2} }{b {}^{2} } = \frac{9}{25} \: ............(taking \: squre \: root) \\ \\ \frac{a}{b} = \frac{3}{5}$
I hope this will helps you..

Thanks.