Question

# The equation x(log2x)2−(11/2)log2x+(17/2)=8 has

A
at least one real solution.
B
exactly three real solutions.
C
exactly one irrational solutions.
D
Exactly two real solutions.

Solution

## The correct options are A at least one real solution. B exactly three real solutions. C exactly one irrational solutions.x(log2x)2−(11/2)log2x+(17/2)=8 x(log2x)2−(11/2)log2x+(17/2)=23 {(log2x)2−(11/2)log2x+(17/2)}(log2x)=3 Let log2x=t, then (t2−112t+172)t=3 2t3−11t2+17t−6=0 ⇒(t−2)(t2−72t+32)=0 ⇒(t−2)(t−12)(t−3)=0 ⇒t=12, 2, 3 ⇒log2x=12, 2, 3 x=√2, 4, 8

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