Question

x/2 + 1 = 12/x
it is a quadratic equation please solve this and tell the answer​

Answer 1

$\sf \frac{x}{2} + 1 = \frac{12}{x}$

$\sf \implies x( \frac{x}{2} + 1) = 12$

$\sf \implies\frac{ {x}^{2} }{2} + x = 12$

$\sf \implies\frac{ {x}^{2} + 2x }{2} = 12$

$\sf \implies{x}^{2} + 2x = 24$

$\sf \implies{x}^{2} + 2x - 24 = 0$

$\sf \implies{x}^{2} - 4x + 6x- 24 = 0$

$\sf \implies x(x - 4) + 6(x-4) = 0$

$\sf \implies (x + 6)(x-4) = 0$

By zero product rule,

$\sf x = - 6 \: or \: x = 4$

Hence, the required answer is,

x=-6,4.

Answer 2

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Q1) x/2+1=12/x

$\large\underline{\sf{Answer}}$

$\: \boxed{ \rm{ \frac{x}{2} + 1 = \frac{12}{x}....... given \: equation }}$

$\: \: \implies \displaystyle \tt{ \frac{x}{2} + 1 = \frac{12}{x}}$

$\: \implies \displaystyle \tt{x + 2 = \frac{24}{x} }$

$\: \implies \displaystyle \tt{ {x}^{2} + 2x = 24}$

$\: \implies \displaystyle \tt{ {x}^{2} + 2x - 24} = 0$

$\: \implies \displaystyle \tt{ {x}^{2} + 6x - 4x - 24 = 0}$

$\: \implies \displaystyle \tt{x(x + 6) - 4(x + 6) = 0}$

$\: \implies \displaystyle \tt{(x + 6)(x - 4) = 0}$

$\: \\ \divideontimes \underline{\displaystyle \tt{x = - 6 \: and \: x = 4 \: is \: the \: solution}}$

$\: \boxed{ \sf{this \: is \: a \: quadratic \: equation \: of \: degree \: 2}}$