Question

X+1÷x=3,x≠o using quadratic formula

Answer 1

Answer:

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

Step-by-step explanation:

Given that ;

$\sf \implies x + \dfrac{1}{x} = 3$

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,

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