Question

find the roots of
$x + \frac{1}{x} = \frac{13}{6}$
by factorisation method
solve it brainly users
challenge​

Answer 1

Answer:

x=3/2,2/3

Step-by-step explanation:

use formula to find root of quadratic equation.

then we find roots are

3/2 and 2/3

Answer 2

$\star\:\:\bf\large\underline\blue{Question:-}$

• Find the roots of the equation
• $x + \frac{1}{x} = \frac{13}{6}$

$\star\:\:\bf\large\underline\blue{Solution:-}$

$x + \frac{1}{x} = \frac{13}{6}$

$\implies \frac{ {x}^{2} + 1}{x} = \frac{13}{6}$

On Cross Multiplying, we get,

$\implies 6 {x}^{2} + 6 = 13x$

$\implies 6 {x}^{2} + 6 - 13x = 0$

$\implies 6 {x}^{2} - 13x + 6= 0$

$\implies 6 {x}^{2} - 9x - 4x + 6= 0$

$\implies 3x(2x - 3) - 2(2x - 3) = 0$

$\implies (3x - 2)(2x - 3) = 0$

Therefore,

$3x - 2 = 0$

$\implies x = \frac{2}{3}$

Also,

$2x - 3 = 0$

$\implies x = \frac{3}{2}$

$\star\:\:\bf\large\underline\blue{Answer:-}$

The possible solutions are:-

• $\frac{2}{3}$ and

• $\frac{3}{2}$