Question

Which number is a solution of the inequality?
х(7 - x) >8
2
8
о
-1

Answer 1

Explanation:

7x-x^2>8

or x²-7x<-8

adding both sides (-7/2)² or 35/4

for x²-7x+35/4<-8+35/4

(x-7/2)²<(-32+35)/4

or (x-7/2)²<3/4

|x-7/2|<(√3)/2

-(√3)/2<x-7/2<(√3)/2

7/2-(√3)/2<x<7/2+(√3)/2

(7-√3)/2<x<(7+√3)/2

(7-1.732)/2<x<(7+1.732)/2

2.634<x<4.37

so x=2 is a solution.