Question

using properties of proportion, solve for a √7a²+1 +2a/ √7a²+1 - 2a ＝ 7

Answer 1

$\sf{\underline\pink{Question:-}}$

solve for a √7a²+1 +2a/ √7a²+1 - 2a ＝ 7

$\huge{\underbrace{\mathbb{Answer}}}$

don't know

Answer 2

Answer:

$\pm \text{ }3$

Step-by-step explanation:

${\sqrt{7a^{2} + 1 } + 2a \over \sqrt{7a^{2} + 1 } - 2a} = 7$

$\rightarrow {\sqrt{7a^{2} + 1 } + 2a \over \sqrt{7a^{2} + 1 } - 2a} = {7\over1}$

Applying componendo and dividendo...

$\rightarrow {{\sqrt{7a^{2} + 1 } + 2a + (\sqrt{7a^{2} - 1 } + 2a )\over{\sqrt{7a^{2} + 1 } + 2a - (\sqrt{7a^{2} + 1 } - 2a})} = {7+1\over7-1}$

$\rightarrow {{2(\sqrt{7a^{2} + 1 })\over{4a}} = {8\over6}$

$\rightarrow {{(\sqrt{7a^{2} + 1 })\over{2a}} = {4\over3}$

Squaring both sides..

$\rightarrow {7a^2 + 1\over{4a^2}} = {16\over9}$

Cross multiplication...

$\rightarrow {63a^2 + 9} = {64a^2}\\\rightarrow 9 = a^2\\\rightarrow a = \pm\text{ }3$