Theory of Equations 1 Question 30

31. The equation x34(log2x)2+log2x54=2 has

(1989; 2M)

(a) atleast one real solution

(b) exactly three real solutions

(c) exactly one irrational solution

(d) complex roots

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Answer:

Correct Answer: 31. (b)

Solution:

  1. Given, x34(log2x)2+log2x54=2

34(log2x)2+log2x54=logx2

34(log2x)2+log2x54=12log2x

3(log2x)3+4(log2x)25(log2x)2=0

Put log2x=y

3y3+4y25y2=0

(y1)(y+2)(3y+1)=0

y=1,2,1/3

log2x=1,2,1/3

x=2,121/3,14



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