Question

If X is real , then expression X+2 / 2x²+3x+6 takes all values in the interval of

Answer 1

Answer:

y = [-1/13,1/3]

step by step explanation:

Given,

x+2/(2x^2 +3x+6)

if : y= x+2/(2x^2+3x+6)

⇒2yx^2+3yx+6y=x+2

⇒2yx^2+3yx+6y−x−2=0

⇒2yx^2 +3yx+6y−x−2=0

⇒2yx^2+(3y−1)x+6y−2=0

here,xisrealno.andD≥0

⇒(3y−1)^2−4(2y)(6y−2)≥0

⇒9y^2+1−6y−8y(6y−2)≥0

⇒9y^2+1−6y−48y^2+16y)≥0

⇒−39y^2+10y+1≥0

⇒39y^2−10y−1≤0

⇒39y^2 −13y+3y−1≤0

⇒13y(3y−1)+1(3y−1)≤0

⇒(3y−1)(13y+1)≤0

∴y=[ -1/13,1/3 ]