Question

Given that a= (5/2n) and b= (2n - 1 / 6). If a = b, find the values of n.

Answer 1

Step-by-step explanation:

According to the Question

$a = b$

$\frac{5n}{2n} = \frac{2n - 1}{6}$

$by \: cross \: multiplication$

$30 = 4 {n}^{2} - 2n$

$rearranging \: the \: terms$

$4 {n}^{2} - 2n - 30 = 0$

Comparing the equation with general form..

$a = 4 \: \: \: \: b = - 2 \: \: \: \: c = - 30$

Applying Quadratic formula and Substituting the terms..

$\frac{2 + - \sqrt{4 - 4(2)( - 15)} }{2(4)}$

$\frac{2 + - \sqrt{484} }{8}$

$\frac{2 + 22}{8} \: and \: \frac{2 - 20}{8}$

$3 \: and \: \frac{ - 18}{8}$