Are there any two real nonzero numbers a and b

gea3stwg

gea3stwg

Answered question

2022-01-29

Are there any two real nonzero numbers a and b such that a2+ab+b2=0 Why or why not?

Answer & Explanation

Gwendolyn Meyer

Gwendolyn Meyer

Beginner2022-01-30Added 11 answers

Step 1
Fix b0 and try to solve in a. This a second order equations so the possible values of a in terms of b are
a1,2=b3b22
So, for any non zero real value b the possible values of a are complex conjugated because
3b2<0
Therefore you cannot find two non-zero reals such that
(a+b)2=ab
sphwngzt

sphwngzt

Beginner2022-01-31Added 11 answers

Step 1
a2+ab+b2
=b2((ab)2+ab+1)
=0
so letting
x=ab
we get the quadratic equation
x2+x+1=0
which has no real roots.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?