Question

if x^2-4/x^2=3 then x =​

Answer 1

Answer:

2

Step-by-step explanation:

 ⇒ x^2 - 4/x^2 = 3

        Let x^2 = a

⇒ a - 4/a = 3

⇒ ( a^2 - 4 )/a = 3

⇒ a^2 - 4 = 3a

⇒ a^2 - 3a - 4 = 0

⇒ a^2 - ( 4 - 1 )a - 4 = 0

⇒ a^2 - 4a + a - 4 = 0

⇒ a( a - 4 ) + ( a - 4 ) = 0

⇒ ( a - 4 ) ( a + 1 ) = 0

 a = 4 or - 1    ( going with +ve )

a = 4

⇒ x^2 = 4

⇒ x = 2

   

Answer 2

Given:-

${\red{\sf{ {x}^{2} - \frac{4}{ {x}^{2} }} = 2}}$

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To find:-

${\sf{Value~of~x}}$

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Assumption:-

${\sf{Let \: {x}^{2} = y}}$

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Solution:-

${\sf{The \: equation \: can \: be \: written \: as:-}} \\ {\sf{y - \frac{4}{y} = 3}} \\ {\sf{ \frac{ {y}^{2} - 4 }{y} = 3}} \\ {\sf{ {y}^{2} - 4 = 3y}} \\ {\sf{ {y}^{2} - 3y - 4 = 0}} \\ {\sf{ {y}^{2} - 4y + y - 4 = 0}} \\ {\sf{y(y - 4) + 1(y - 4) = 0}} \\ {\sf{(y + 1)(y - 4) = 0}} \\ {\sf{y = - 1~ or \: y = 4}}$

${\sf{As~y~is~square~of~a~no.~x}} \\ {\sf{y ≠ -1}} \\ {\sf{{\therefore}~ y = 4}}$

${\sf{Putting~y = 4~in~{x}^{2} = y}}$

${\sf{x = \sqrt{y}}} \\ {\sf{x = \sqrt{4} }} \\ {\sf{x = 2}}$

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${\therefore}~ \red{\sf{x = 2}}$