MonotonicityHard
Question
Number of solution(s) satistying the equation, 3x2 - 2x3 = log2 (x2 + 1) - log2 x is -
Options
A.1
B.2
C.3
D.none
Solution
3x2 - 2x3 = log2 
, x > 0
f (x) = 3x2 - 2x3
f (x) = 6x - 6x2
= 6x (1 - x)
f (x) ≤ f(1)
f(x) ≤ 1
⇒ LHS ≤ 1&RHS ≥ 1
LHS = RHS = 1 for x = 1
∴ equation has exactly one solution
, x > 0f (x) = 3x2 - 2x3
f (x) = 6x - 6x2
= 6x (1 - x)
f (x) ≤ f(1)
f(x) ≤ 1
⇒ LHS ≤ 1&RHS ≥ 1
LHS = RHS = 1 for x = 1
∴ equation has exactly one solution
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