Question

determine the roots of rhe equation: 10x - 1/x =3​

Answer 1

Heyya...

Solution :-

$10x - \frac{1}{x} = 3$

$\frac{10 {x}^{2} - 1 }{x} = 3$

${10x}^{2} - 1 = 3x$

${10x}^{2} - 3x - 1 = 0$

$5x(2x - 1) + 1(2x - 1) = 0$

$(5x + 1)(2x - 1) = 0$

$5x + 1 = 0$

$x = - \frac{ 1}{5}$

$2x - 1 = 0$

$x = \frac{1}{2}$

$\frac{1}{2} \: and - \frac{1}{5} \: are \: the \: \: two \: \: roots \: of \: equation.$

HOPE HELPFUL....

Answer 2

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10x – 1/x = 3

⇒ 10x2 – 1/x = 3

⇒ 10x2 – 3x – 1 = 0

⇒ 10x2 – 5x + 2x – 1 = 0

⇒ 5x(2x – 1) + 1(2x – 1) = 0

⇒ (2x – 1)(5x + 1) = 0

2x – 1 = 0

or 5x + 1 = 0

x = ½ or x = -1/5 are two roots of the equation.