Question

N(a-b) =b(a+b) find the valu of n

Answer 1

ANSWER

$n(a - b) = b(a +b ) \\ n.a - n.b = ba + {b}^{2} \\ na - ba = {b}^{2} + n.b \\ a(n - b) = b(n + b) \\ \frac{a}{b} = \frac{n + b}{n - b} \\ \\ now \: apply \: componendo \: and \: dividendo \\ \\ \frac{a + b}{a - b} = \frac{n + b + n - b}{n + b - (n - b)} \\ \frac{a + b}{a - b} = \frac{2n}{2b} \\ \\ n = \frac{b(a + b)}{a - b}$

WHAT IS COMPONENDO AND DIVIDENDO?

$suppose \: any \: fraction.... \\ \frac{a}{b} \: which \: is \: equal \: to \: another \\ fraction \: let \: say \: \frac{c}{d} \: than \: acc \: to \\ compo. \: and \: dividendo \\ \\ \frac{a}{b} = \frac{c}{d} \\ \\ \frac{a + b}{a - b} = \frac{c + d}{c - d}$