Question

(
2x^2 - 6x +5/
x² – 3x+2

Find the range of the following expression​

Answer 1

Answer:

y=

2x

2

+3x+6

x+2

⇒ 2yx

2

+3yx+6y=x+2

⇒ 2yx

2

+(3y−1)x+6y−2=0 (i)

case I: if y



=0, then equation (i) is quadratic in x

∵ x is real

∴ D≥0

⇒ (3y−1)

2

−8y(6y−2)≥0

⇒ (3y−1)(13y+1)≤0

yϵ[−

13

1

,

13

1

]−{0}

case II: if y=0, then equation becomes

x=−2 which is possible as x is real

∴ Range yϵ[−

13

1

,

3

1

]