Math, asked by devisapkota124, 10 months ago

How to simplify ( x+2)-1/x+2=5

Answers

Answered by Mihir1001

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$Answer:$

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$Step-by-step-explaination:$

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We have,

$(x + 2) - \frac{1}{x + 2} = 5$

$\implies \frac{(x + 2)(x + 2) - 1}{x + 2} = 5$

$\implies \frac{ {(x + 2)}^{2} - 1}{1} = 5 \times (x + 2)$

$\implies {x}^{2} + 4x + 4 - 1 = 5(x + 2)$

$\implies {x}^{2} + 4x + 3 = 5x + 10$

$\implies {x}^{2} - 5x + 4x - 10 + 3 = 0$

$\implies {x}^{2} - x - 7 = 0$

This equation is of the form $\bold{a {x}^{2} + bx + c = 0}$ ,

where, a = 1 , b = - 1 and c = - 7

Now,

Discriminant,

$D = {b}^{2} - 4ac$

$\implies D = {( - 1)}^{2} - 4(1)( - 7)$

$\implies D = 1 + 28$

$\implies D = 29$

Thus, D > 0

Then, the roots are real and unequal.

Henceforth,

$x = \frac{ - b - \sqrt{D} }{2a} = \frac{ - ( - 1) - \sqrt{29} }{2(1)} = \frac{1 - \sqrt{29} }{2}$

or,

$x = \frac{ - b + \sqrt{D} }{2a} = \frac{ - ( - 1) + \sqrt{29} }{2(1)} = \frac{1 + \sqrt{29} }{2}$

Hence,

$\huge\bold{x = \frac{1 - \sqrt{29} }{2} }$ or $\huge\bold{x = \frac{1 + \sqrt{29} }{2} }$

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