In `Delta ABC` if `AB = x, BC = x + 1, angleC = (pi)/(3)`, then the less integer value of x is

Options

A. 6
B. 7
C. 8
D. none of these

Answer

B

Explanation

Using cosine rule, we get
`x^(2) = (x + 1)^(2) + b^(2) -2 (x + 1) b cos.(pi)/(3)`
`rArr 0 = 2x + 1 + b^(2) - (x +1) b`
`rArr b^(2) -(x +1) b + 2x + 1 = 0`
Since b is real, we have
`rArr (x + 1)^(2) - 4 (2x +1) ge 0`
`rarr x^(2) -6x - 3 ge 0`
`rArr x ge 3 + sqrt12`
The least integral value of x is 7