Question

Solve by using the method of completing the square method :

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

Answer 1

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

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

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

⇒ 2x^2 - 5x + 2 =0

⇒ 2x^2 - 5x = - 2

Step 1 : Dividing both sides by the coefficient of x^2.

⇒ $\dfrac{2x^2}{2} - \dfrac{5x}{2} = \dfrac{-2}{2}$

⇒ x^2 - $\dfrac{5}{2}x = - 1$

Step 2 : Adding the square of product of 1 / 2 and the co efficient of x to both sides.

⇒ x^2 - $\dfrac{5}{2}x + \bigg( \dfrac{5}{4} \bigg)^2 = - 1 + \bigg( \dfrac{5}{4} \bigg)^2$

From the identities of factorization, we know, a^2 - 2ab + b^2 = ( a - b )^2.

∴ $\bigg( x - \dfrac{5}{4} \bigg)^2 = - 1 + \dfrac{25}{16}$

⇒ $\bigg( x - \dfrac{5}{4} \bigg)^2 = \dfrac{-16+25}{16}$

⇒ $\bigg( x - \dfrac{5}{4} \bigg)^2 = \dfrac{9}{16}$

⇒ $\bigg( x - \dfrac{5}{4} = \dfrac{3}{4}\:\:or\:\: -\dfrac{3}{4}$

⇒ x = 3 / 4 + 5 / 4     or     - 3 / 4 + 5 / 4

⇒ x = 8 / 4      or - 2 / 4

⇒ x = 2      or  - 1 / 2

Therefore the value of x is 2 or - 1 / 2 .

Answer 2

Ｈｅｌｌｏ!!!!

Ɋㄩ乇丂ㄒ丨ㄖ几:-
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Solve by using the method of completing the square method :

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

$๏ℓµţɨ๏ɲ :
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Ⓖⓘⓥⓔⓝ Ⓣⓗⓐⓣ,

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

$\bf \: Multiplying \: by \: x^2 \: We \: get,$

$\bf=> 2 - 5x + 2x^2 = 0$

$\bf=> 2x^2 - 5x + 2 = 0$

$\bf=> 2x^2 - 4x - x + 2 = 0$

$\bf=> 2x (x - 2) - (x - 2) = 0$

$\bf=> (x - 2) (2x - 1) = 0$

$\bf \: Hence, \: x = 2 \: or \: x = \frac{1}{2}$

ⱧØ₱Ɇ ł₮ ⱧɆⱠ₱₴!!!!