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If x + 1 = 1 ,then ( x + 1 )5 + 1 equals x + 1 ( x + 1 )5
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Correct Option: B
| x + | = 1 | ||
| x + 1 |
Adding 1 on both sides ,
| ⇒ ( x + 1 ) + | = 2 | |
| ( x + 1 ) |
On squaring,
| ⇒ ( x + 1 )2 + | + 2 = 4 | |
| ( x + 1 )2 |
| ⇒ ( x + 1 )2 + | = 2 ...(i) | |
| ( x + 1 )2 |
| Again, cubing , ( x + 1 ) + | = 2 | |
| ( x + 1 ) |
| ⇒ ( x + 1 )3 + | + 3 |  | ( x + 1 ) + |  | = 8 | ||
| ( x + 1 )3 | ( x + 1 ) |
| ⇒ ( x + 1 )3 + | = 8 – 3 × 2 = 2 | |
| ( x + 1 )3 |
| ∴ | | ( x + 1 )2 + | | | ( x + 1 )3 + | | = 2 × 2 = 4 | ||
| ( x + 1 )2 | ( x + 1 )3 |
| ⇒ ( x + 1 )5 + | | ( x + 1 ) + | | + | = 4 | ||
| ( x + 1 ) | ( x + 1 )5 |
| ⇒ ( x + 1 )5 + | = 4 – 2 = 2 | |
| ( x + 1 )5 |
Second method :
| Here, x + | = 1 | ||
| x + 1 |
| ⇒ ( x + 1 ) + | = 2 | |
| ( x + 1 ) |
| ∴ ( x + 1 )2 + | = 2 | |
| ( x + 1 )2 |
