Question

WHat is the solution of x^2 + x-6 / x-7 < 0

Answer 1

A

Explanation:

`(x^2+x-6)/(x-7) \leq 0\\`

hence numerator and denominator are of opposite sign.

case1 .

let x²+x-6≥ 0

and x-7<0

x²+x≥6

x²+x+1/4≥6+1/4

(x+1/2)²≥25/4

(x+1/2)²≥(5/2)²

|x+1/2|≥5/2

x+1/2≥5/2

x≥5/2-1/2

x≥2

or

x+1/2≤-5/2

x≤-5/2-1/2

x≤-3

also x-7<0

x<7

combining

x≤-3 or 2≤x<7

case 2.

x²+x-6<0

and x-7≥0

x²+x<6

x²+x+1/4<6+1/4

(x+1/2)²<25/4

|x+1/2|<5/2

so -5/2 <x+1/2<5/2

-5/2-1/2<x<5/2-1/2

-3<x<2

also x-7≥0

so x≥7

combining

we get no vlaue satisfying both the values.

Hence rejected.

Answer 2

x≤-3 or 2≤x∠7

Explanation:

It would be the first answer on the paper