Solve the following equation for x. x+3 x−2 − 1−x x = 17 4 ;x≠0,2

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Solve the following equation for x.

$x + 3 x − 2 − 1 − x x = 174; x ≠ 0, 2$

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x is

4, − 29

x is

5, − 29

x is

4, − 19

x is

4, − 27

answer is A.

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Detailed Solution

Given equation is

x + 3 x − 2 − 1 − x x = 174; x ≠ 0, 2.

In quadratic equation,

a x 2 + b x + c = 0 (a ≠ 0)

Discriminant,

D = b 2 − 4 a c

Root of quadratic equation,

x = − b ± D 2 a .

On simplifying the given equation we get,

x + 3 x − 2 − 1 − x x = 174 x 2 + 3 x − x + x 2 + 2 − 2 x x 2 − 2 x = 174 4 2 x 2 + 2 = 17 x 2 − 2 x 8 x 2 + 8 = 17 x 2 − 34 x 9 x 2 − 34 x − 8 = 0

Now let us find the roots using the quadratic formula.

x = − (− 34) ± (− 34) 2 − 4 (9) (− 8) 2 (9) x = 34 ± 1444 18 x = 34 ± 38 18 x = 34 + 38 18, 34 − 38 18 x = 4, − 2 9

The value of x is

4, − 29 .

The correct option is (1).

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