# If -6b+2a-25 = 5 and a/b + 6 = 4, what is the value of (b/a)square?

Feb 27, 2018

$- 6 b + 2 a - 25 = 5$

$\implies 2 a - 6 b = 30 \implies a - 3 b = 15$

=>a=3b+15 -> color(red)(1

color(white)(b=-3

$\frac{a}{b} + 6 = 4$

$\implies \frac{3 b + 15}{b} + 6 = 4$ (Replacing $a$ from $\textcolor{red}{1}$)

$\implies 3 + \frac{15}{b} = - 2$

$\implies \frac{15}{b} = - 5$

=>color(magenta)(b=-3

Now, coming to $a$, $a = 3 b + 15$
$\implies a = 3 \left(- 3\right) + 15$
=>color(magenta)(a= 6

To find ; ${\left(\frac{b}{a}\right)}^{2} = {\left(- \frac{3}{6}\right)}^{2} = {\left(- \frac{1}{2}\right)}^{2} = \frac{1}{4}$

color(white)(b=-3

Alternatively ,
Form the equation, $\frac{a}{b} + 6 = 4$

$\frac{a}{b} = - 2$

$\frac{b}{a} = \frac{- 1}{2}$

and then, squaring both the sides, we would get,

${\left(\frac{b}{a}\right)}^{2} = {\left(\frac{- 1}{2}\right)}^{2} = \frac{1}{4}$

That's a comparatively shorter approach :)
Hope it helps.