# How can I prove that a + b = c = 0?

#### Ayylien64

##### New member
Hi. I've got an exercise and it says:

Rational numbers a, b, c satisfy the equation
(a + b +c)(a + b - c) = c[SUP]2[/SUP]
Prove that a + b + c = 0

I don't know how to prove this. I overall don't know how to prove any equations in math. Can you help me with that?

#### Subhotosh Khan

##### Super Moderator
Staff member
Hi. I've got an exercise and it says:

Rational numbers a, b, c satisfy the equation
(a + b +c)(a + b - c) = c[SUP]2[/SUP]
Prove that a + b + c = 0

I don't know how to prove this. I overall don't know how to prove any equations in math. Can you help me with that?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

http://www.freemathhelp.com/forum/announcement.php?f=33

#### pka

##### Elite Member
Rational numbers a, b, c satisfy the equation
(a + b +c)(a + b - c) = c[SUP]2[/SUP]
Prove that a + b + c = 0
Do you know that $$\displaystyle (x+y)(x-y)=x^2-y^2~?$$ Do you know the value of $$\displaystyle x$$ if $$\displaystyle x^2=0~?$$

#### pka

##### Elite Member
u = a + b
(u + c)(u - c) = c^2
u^2 - c^2 = c^2
2c^2 = u^2
c = u / SQRT(2)
Right. Note a,b, & c are rational numbers.