Question

solve the equation b completing square a^2x^2=axb+2b^2

Answer 1

Step-by-step explanation:

We have,

${a}^{2} {x}^{2} = abx + 2 {b}^{2}$

$\implies {a}^{2} {x}^{2} - abx - 2 {b}^{2} = 0$

$\implies {a}^{2} {x}^{2} - abx + \frac{ {b}^{2}}{4} - 2 {b}^{2} - \frac{ {b}^{2} }{4} = 0$

$\implies(ax - \frac{b}{2} )^{2} - \frac{9 {b}^{2} }{4} = 0$

$\implies(ax - \frac{b}{2} ) = \frac{3b}{2} \: \: or \: \: (ax - \frac{b}{2} ) = - \frac{3b}{2}$

$\implies \: x = \frac{2b}{a} \: \: or \: \: x = - \frac{b}{a}$