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Solve the following quadratic equations by factorization:

$x − 1 x − 3 = 3, x ≠ 0$

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5 ± 27

3 ± 27

3 ± 210

3 ± 10

answer is D.

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Detailed Solution

Given: x − 1 x − 3 = 3, x ≠ 0

⇒ x 2 − 1 x = 3 + 3 ⇒ x 2 − 1 = 6 x ⇒ x 2 − 6 x − 1 = 0 … … (1)

Use the formula

x = − b ± b 2 − 4 a c 2 a

in equation (1) to solve for x.

⇒ x = − (− 6) ± (− 6) 2 − 4 (1) (− 1) 2 (1) ⇒ x = 6 ± 36 + 4 2 ⇒ x = 6 ± 210 2 ⇒ x = 3 ± 10

The solutions of the quadratic equation are:

⇒ x = 3 + 10 ⇒ x = 3 − 10

So, the correct option is 4.

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