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If x + 1 = √3 the value of (x18 + x12 + x6 + 1) is x
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Correct Option: A
| x + | = √3 | |
| x |
On cubing both sides,
| ⇒ |  | x + |  | 3 | = (3√3)3 | |
| x |
| ⇒ x3 + | + 3x. | | x + | | = 3√3 | |||
| x3 | x | x |
| ⇒ x3 + | + 3 × √3 = 3√3 | |
| x3 |
| ⇒ x3 + | = 3√3 - 3√3 = 0 | |
| x3 |
⇒ x6 + 1 = 0
∴ x18 + x12 + x6 + 1 = x12( x6 + 1 ) + 1( x6 + 1 )
x18 + x12 + x6 + 1 = ( x6 + 1 )( x12 + 1 ) = 0
