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

Ayylien64

New member
Joined
Oct 9, 2016
Messages
2
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
Joined
Jun 18, 2007
Messages
18,089
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?
What are your thoughts?

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

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You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

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

pka

Elite Member
Joined
Jan 29, 2005
Messages
7,686
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
Joined
Jan 29, 2005
Messages
7,686
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.
 
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