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Question

Given that, for all real x, the expression x2+2x+4x22x+4 lies between 13 and 3. The values between which the expression 9.32x+6.3x+49.32x6.3x+4 lies are


A

1 and 1

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B

13 and 3

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C

0 and 2

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D

2 and 0

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Solution

The correct option is B

13 and 3


As given in the question,
13<x2+2x+4x22x+4<3 for all xR . . . (1)

Let 3x+1=y,

Then yR for all xR.

9.32x+6.3x+49.32x6.3x+4

32x+2+2.3x+1+432x+22.3x+1+4

y2+2y+4y22y+4

From (1)

13<y2+2y+4y22y+4<3

13<9.32x+6.3x+49.32x6.3x+4<3


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