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X+1÷x=3,x≠o using quadratic formula

Answer»

Answer:

\large{\underline{\boxed{\sf x = \frac{3 + \sqrt{5} }{2} \: \: or \: \: x = \frac{3 - \sqrt{5} }{2}}}}

Step-by-step EXPLANATION:

GIVEN that ;

\sf \implies x + \dfrac{<klux>1</klux>}{x} = 3

On solving the problem, we get -

\sf \implies x + \dfrac{1}{x} = 3 \\ \\ \sf \implies \frac{x {}^{2} + 1 }{x} = 3 \\ \\ \sf \implies {x}^{2} + 1 = 3x \\ \\ \sf \implies x {}^{2} - 3x + 1 = 0

Now, we got a quadratic equation, on COMPARING the given equation with ax² + bx + C = 0, we get -

  • a = 1
  • b = - 3
  • c = 1

Discriminant = b² - 4ac

⇒ D = (-3)² - 4 * 1 * 1

⇒ D = 9 - 4

⇒ D = 5

\tt x = \frac{ - b \pm \sqrt{D} }{2a} \\ \\ \tt \implies x = \frac{ - ( - 3) \pm \sqrt{5} }{2 \times 1} \\ \\ \tt \implies x = \frac{3 \pm \sqrt{5} }{2}

Therefore,

\boxed{ \bf x = \frac{3 + \sqrt{5} }{2} \: \: or \: \: x = \frac{3 - \sqrt{5} }{2}}


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