यदि `x = 1/(2-sqrt(3))`, तो `x^(3) - 2x^(2) - 7x + 5` का मान ज्ञात कीजिए।

Options

A. `3`
B. `2`
C. `1`
D. `0`

Answer

A

Explanation

यहाँ
`x = 1/(2-sqrt(3)) = 1/(2+sqrt(3)) xx (2sqrt(3))/(2+sqrt(3)) = (2+sqrt(3))/((2)^(3) -(sqrt(3))^(2)) = 2+sqrt(3)`
`rArr (x-2) = sqrt(3)`
दोनों पक्षों का वर्ग करने पर
`(x-2)^(2) = (sqrt(3))^(2)`
`rArr x^(2) - 4x + 4 = 3`
`rArr x^(2) - 4x + 1 = 0`
अब, `x^(3) - 2x^(2) - 7x+ 5 = x (x^(2) - 4x+ 1) + 2x^(2) - 8x + 5`
`= x(x^(2) - 4x + 1) + 2 (x^(2) - 4x +1) + 3`
`= x (0) + 2(0) + 3` [(1)से]
`= 3`