The equation ` sqrt(1+log_(x) sqrt27) log_(3) x+1 = 0` has

Options

A. no integral solution
B. one irrational solution
C. two real solutions
D. no prime solution

Answer

A, D

Explanation

` (sqrt(1+3/(2log_(3)x))) log_(3) x +1 = 0`
Let ` log_(3) x = y" we get "`
`(sqrt(1+3/(2y)))y =- 1`
` or (1+3/(2y)) = 1/y^(2)`
` or (2y+3)/(2y)= 1/y^(2)`
` or 2y^(2) + 3y-2= 0 (.:' y ne 0)`
` or 2y^(2) + 4y-y - 2 = 0`
` or (y+2)(2y-1)=0`
` y = 1//2 or y =- 2 ` (not possible)
` rArr x = 3^(1//2)`