Question

please solve the problem.​

Answer 1

Question -

Factorise -

$\frac{2}{ {x}^{2} } - \frac{5}{x} + 2 = 0$

Answer -

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

Step-by-step explanation:

1) Multipy both sides by the common denominator - x

$\frac{2}{ {x}^{2} } \times x - \frac{5}{x} \times x + 2 \times x = 0 \times x$

$\frac{2}{x} - 5 + 2x = 0$

2) Multipy both sides by x

$\frac{2}{x} \times x - 5 \times x + 2x \times x = 0 \times x$

$2 - 5x + 2 {x}^{2} =0$

$2 {x}^{2} - 5x + 2 = 0$

3) By doing middle term factorisation

$2 {x}^{2} - (4 + 1)x + 2 = 0$

$2 {x}^{2} - 4x - x + 2 = 0$

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

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

4) Value for x

Either,

$x - 2 = 0 \\ x = 2$

Or,

$(2x - 1) = 0 \\ 2x = 1 \\ x = \frac{1}{2}$

Therefore x = 2 and 1/2