Question

Find the roots of 3x-2 = 8/x​

Answer 1

$\large\underline\purple{\bold{Solution :- }}$

$\tt \ \: :  ⟼ 3x - 2 = \dfrac{8}{x}$

$\tt \ \: :  ⟼ {3x}^{2} - 2x = 8$

$\tt \ \: :  ⟼ 3 {x}^{2} - 2x - 8 = 0$

$\tt \ \: :  ⟼ {3x}^{2} - 6x + 4x - 8 = 0$

$\tt \ \: :  ⟼ 3x(x - 2) + 4(x - 2) = 0$

$\tt \ \: :  ⟼ (x - 2)(3x + 4) = 0$

$\tt \ \: :  ⟼ x - 2 = 0 \: or \: 3x + 4 = 0$

$\tt \ \: :  ⟼ x = 2 \: or \: x = - \dfrac{4}{3}$

Answer 2

HEYAA!!!

let's arrange in order!!

$3x + \frac{8}{x} - 2 = 0$

$3 {x}^{2} - 2x - 8 = 0$

$3 {x }^{2} - 6x + 4x - 8 = 0$

$3x(x - 2) + 4(x - 2) = 0$

$(3x + 4)(x - 2) = 0$

HENCE

$x = \frac{ - 4}{3} or \: x = 2$