F.4 AM

a) a>0

x^2-1>0

x>1

b>0

2x+1>0

x>-1/2

a+b>c

x^2 -1+2x+1>x^2+x+1

x>1

so,x>1.

b)c - a

x^2 + x + 1 - x^2 +1

= x + 2

since x > 1 ,x + 2 must be positive, so c > a

a>b ??? 係咪打錯題目

代x = 2 , 2^2 -1 = 3 , 2x+1 = 5 = =

c) The largest angle of triangle ABC is angle C.

cos C = a^2 + b^2 - c^2 / 2ab
cos C = (x^2 -1 )^2 + (2x+1)^2 - (x^2+x+1)^2 / 2(x^2 -1)(2x+1)
cos C = x^4 -2X^2 + 1 + 4X^2 + 4x + 1 -x^4 -x^3 - x^2 -x^3 - x^2 -x - x^2 - x -1 / 4x^3 - 4x + 2x^2 - 2
cos C = -x^2 + 2x -2x^3 + 1/ -2(-x^2+2x -2x^3+1)
cos C = -1/2

C = 120*