# Simple solution?

1. Aug 20, 2008

### eskil

just looking for a quick solution for my equation, seems like my head is just working the wrong way coz I know it's not a hard one:

a2 + a2 = (a + 1)2

a = ?

2. Aug 20, 2008

### rock.freak667

a2+a2=2a2
expand the right side and then simplify.

3. Aug 20, 2008

### eskil

i don't believe that (a + 1)(a + 1) is 2a2
shouldn't that give a2 + 2a +1 ??

4. Aug 20, 2008

### NoMoreExams

$$a^{2} + a^{2} = (a+1)^{2}$$ simplifies to $$a^{2} + a^{2} = a^{2} + 2a + 1$$ which when you move everything over to one side becomes $$a^{2} - 2a - 1 = 0$$ which is easy enough to solve. Not sure how rock.freak got what he did.

Last edited: Aug 20, 2008
5. Aug 20, 2008

### snipez90

I'm sure he was simplifying the left side (how much simpler can it be?). Then he said expand the RHS and rearrange to solve.

6. Aug 20, 2008

### eskil

solved it now

a2 + a2 = a2 + 2a + 1

0 = -a2 + 2a + 1

a1 = 1 + sq.root of 2
a2 = 1 - sq.root of 2

a2 is negative therefore a1 is the right answer

which gives a = 2,41

7. Aug 20, 2008

### NoMoreExams

Why can't a be negative?

On the LHS you had $$a^{2} + a^{2} = (1 - \sqrt{2})^{2} + (1 - \sqrt{2})^{2} = 1 - 2 \sqrt{2} + 2 + 1 - 2 \sqrt{2} + 2 = 6 - 4 \sqrt{2}$$

However on the RHS you had $$(a+1)^{2} = (1 - \sqrt{2} + 1)^{2} = (2 - \sqrt{2})^{2} = 4 - 4 \sqrt{2} + 2 = 6 - 4 \sqrt{2}$$

Note also that the "simpler" way to do this would be to rewrite it as

$$2a^{2} = (a+1)^{2} \Rightarrow \sqrt{2} |a| = |a + 1|$$ and examine the appropriate regions to get rid of | |.

8. Aug 20, 2008

### eskil

The reason why it cannot be negative is that the origin of the problem was to determine the length of all sides of a likesided triangle thus can't be negative.

I still think that using the quadratic equation is the simplest way of solving it.