If x is real, then the value of the expression (x2+34 x-71/x2+2 x-7) does not exist between -

Question

If x is real, then the value of the expression (x2+34 x-71/x2+2 x-7) does not exist between - (A) -5 and 9 (B) 5 and -9 (C) -5 and -9 (D) 5 and 9

Tardigrade Admin · Accepted Answer

(x2+34 x-71/x2+2 x-7)=y x2(1-y)+x(34-2 y)-71+7 y=0 x ∈ R D ≥ 0 4(17-y)2-(7 y-71)(1-y) ≥ 0 (17-y)2-[7 y-7 y2-71+71 y] ≥ 0 289+y2-34 y-7 y+7 y2+71-71 y ≥ 0 8 y2-112 y+360>0 y2-14 y+45 ≥ 0 (y-5)(y-9) ≥ 0 y does not lie b/w 5 9

Q. If $x$ is real, then the value of the expression $\frac{x ^{2} + 34 x - 71}{x ^{2} + 2 x - 7}$ does not exist between -

$- 5$ and 9

5 and -9

-5 and -9

5 and 9

Q. If x is real, then the value of the expression x2+2x−7x2+34x−71​ does not exist between -

−5 and 9

5 and -9

-5 and -9

5 and 9

x2+2x−7x2+34x−71​=y x2(1−y)+x(34−2y)−71+7y=0 x∈RD≥0 4(17−y)2−(7y−71)(1−y)≥0 (17−y)2−[7y−7y2−71+71y]≥0 289+y2−34y−7y+7y2+71−71y≥0 8y2−112y+360>0 y2−14y+45≥0 (y−5)(y−9)≥0 y does not lie b/w 5&9

Q. If $x$ is real, then the value of the expression $\frac{x ^{2} + 34 x - 71}{x ^{2} + 2 x - 7}$ does not exist between -

$- 5$ and 9