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Question

Given that for all real values of x, the expression x2+2x+4x22x+4 lies between 13 and 3. Then the values of the expression 4x+2x+14x2x+1 lie between

A
13 and 3
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B
1 and 0
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C
1 and 1
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D
0 and 7
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Solution

The correct option is A 13 and 3
4x+2x+14x2x+1
=(2x)2+2x+1(2x)22x+1
=4(2x)2+4(2x)+44(2x)24(2x)+4=(2x+1)2+2(2x+1)+4(2x+1)22(2x+1)+4

Let 2x+1=t
Then, (2x+1)2+2(2x+1)+4(2x+1)22(2x+1)+4=t2+2t+4t22t+4
So, given expression has values lying in between 13 and 3.

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