Manipal Entrance Test 2019 Math Paper

We have,

x+1

x2+2

>

1

4

⇒x2+2−4x−4<0
⇒x2−4x−2<0
⇒(x−2)2−(√6)2<0
⇒{(x−2)−√6)}(x−2+√6)<0
⇒2−√6<x<2+√6
⇒2−2.449<x<2+2.449
⇒−0.449<x<4.449
∴ In between - 0.445 and 4.449 five values of x lies, i.e. 0, 1, 2, 3, 4.
∴ There are 5 integral solution of inequality.