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Solve the following quadratic equations by factorization:

$x + 1 x − 1 − x − 1 x + 1 = 56, x ≠ 1, − 1$

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x = 5, 15

x = 5, − 15

x = 5, 25

x = 4, 25

answer is B.

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Detailed Solution

Given,

x + 1 x − 1 − x − 1 x + 1 = 56, x ≠ 1, − 1

⇒ 4 x x 2 − 1 = 56 ⇒ 5 x 2 − 5 = 24 x ⇒ 5 x 2 − 24 x − 5 = 0 ⇒ 5 x 2 − 25 x + x − 5 = 0

⇒ 5 x (x − 5) + 1 (x − 5) = 0 ⇒ (x − 5) (5 x + 1) = 0 ⇒ x − 5 = 0 or 5 x + 1 = 0 ⇒ x = 5 or x = − 1 5

For the equation x + 1 x − 1 − x − 1 x + 1 = 56, the roots are x = 5 and x = − 1 5 .

Hence, the correct option is 2.

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