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Question

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


Correct Answer
A
at least one real solution.
Correct Answer
B
exactly three real solutions.
Correct Answer
C
exactly one irrational solutions.
Your Answer
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
(t2112t+172)t=3
2t311t2+17t6=0
(t2)(t272t+32)=0
(t2)(t12)(t3)=0
t=12, 2, 3
log2x=12, 2, 3
x=2, 4, 8

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