How many distinct solutions does the following equation have? log(base x^2 +2) (4-5x^2 - 6x^3) = 2 a)None, b)1, c)2, d)4, e)Infinitely many
log(base x2 +2) (4-5x2 - 6x3) = 2 is equivalent to 4-5x2-6x3=(x2+2)2 Therefore, we are looking for solutions to the equation 4 - 5x2 - 6x3 = x4 + 4x2 + 4 => x4 + 6x3 + 9x2 = 0 => x2(x2+ 6x + 9) = 0 => x2(x+3)2= 0 Therefore, the equation has 2 distinct solutions. => The answer is c).
