a,b,c are edges of triangle,

prove that the equation: ax^2+2(b+c)x+a=0 . has two distinct real root

and my answer is:prove that the equation: ax^2+2(b+c)x+a=0 . has two distinct real root

a,b,c are edges therefore they are absolute values.

so

a>0

b>0

c>0

also

Δ=4(b+c)^2-4a^2

and I need to prove that Δ>0

so

4(b+c)^2-4a^2>0

which led me for:

(b+c)^2>a^2

b+c>a

now if so far i'm correct, than all I've to do is say that because of triangle inequality "b+c>a" is correct.

And I done with the proving.so

a>0

b>0

c>0

also

Δ=4(b+c)^2-4a^2

and I need to prove that Δ>0

so

4(b+c)^2-4a^2>0

which led me for:

(b+c)^2>a^2

b+c>a

now if so far i'm correct, than all I've to do is say that because of triangle inequality "b+c>a" is correct.