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If x is a rational number and (x + 1)3 - (x - 1)3 = 2 , then the sum of numerator and denominator of x is (x + 1)2 - (x - 1)2
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- 3
- 4
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- 7
- 3
Correct Option: B
| = 2 | ||
| ( x + 1 )2 - ( x - 1 )2 |
| ⇒ | = 2 | |
| ( x2 + 2x + 1 ) - ( x2 - 2x + 1 ) |
| ⇒ | = 2 | |
| x2 + 2x + 1 - x2 + 2x - 1 |
| ⇒ | = 2 | |
| 4x |
| ⇒ | = 1 ⇒ 3x2 + 1 = 4x | |
| 4x |
⇒ 3x2 - 4x + 1 = 0
⇒ 3x2 - 3x - x + 1 = 0
⇒ 3x(x – 1) – 1(x – 1) = 0
⇒ (3x – 1)(x – 1) = 0
⇒ 3x – 1 = 0, or, x – 1 = 0
| ⇒ x = | or 1 | |
| 3 |
Hence, sum of the numerator and denominator = 1 + 3 = 4 or, 1 + 1 = 2
