Question

If x is real, then greatest and least values of x2−x+1x2+x+1x2−x+1x2+x+1 are

Answer 1

Answer:

y=x2+3x+9x2−2x+2

yx2+3xy+9y=x2−2x+2

x2(y−1)+x(3y+2)+9y−2=0

D>0

(3y+2)2−4(9y−2)(y−1)>0

9y2+4+12y−4(9y2−9y−2y+2)>0

36y2−44y+8−9y2−4−12y<0

27y2−56y+4<0

(y−2)(y−272)<0

272<y<2

Step-by-step explanation:

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Answer 2

Answer:

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Step-by-step explanation:

Correct option is

B

2 and

27

2

y=

x

2

+3x+9

x

2

−2x+2

yx

2

+3xy+9y=x

2

−2x+2

x

2

(y−1)+x(3y+2)+9y−2=0

D>0

(3y+2)

2

−4(9y−2)(y−1)>0

9y

2

+4+12y−4(9y

2

−9y−2y+2)>0

36y

2

−44y+8−9y

2

−4−12y<0

27y

2

−56y+4<0

(y−2)(y−

27

2

)<0

27

2

<y<2