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Question

If y=x22x+4x2+2x+4 where x can take real values, then

A
13y3
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B
3<y5
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C
5<y7
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D
7<y9
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Solution

The correct option is A 13y3
y=x22x+4x2+2x+4
x2y+2xy+4y=x22x+4
x2(y1)+2x(y+1)+4y4 =0
Since x is real, D0
4(y+1)24(4y4)(y1)0
4y2+8y+416y2+16y16+16y0
12y2+40y120
3y210y+30
(3y1)(y3)0
Hence, 13y3

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