A funny algebra puzzle!

OK  it's time to publish the official (and right) solution! There are well real solutions for these equations!

From the second equation we can write a = 3/b

Injecting it in the first equation: 9/b² ‐ b² = 9

Or 9 ‐b4 = 9b² or b4 + 9b² ‐ 9 = 0 Let’s pose b²=y

We have then y² + 9y – 9 = 0

And hence y = [‐9 +/‐ (81 +36)1/2]/2 = [‐9+/‐1171/2]/2

Or y = 0.908 and ‐9.908

Since y = b² must be positive, the only value for y is 0.908

Therefore b = +/‐ 0.9531 and a = 3/b = +/‐ 3.1476

There are 2 sets of possible solutions:

Values for a, b are thus :

‐3.1476 and ‐0.9531

And +3.1476 and +0.9531

Big applause to our 4 first winners:

1. Gaetano PIARINO, Key Account Manager - ADI - Milan, Italy

2. Ricardo HABRE, Field Application Engineer - ADI - Farmington (MI), USA

3. Mark CEE, Senior Engineer, Systems Integration Engineering – ADI – Cavite, Philippines

4. Martin WALKER, Product Marketing Lead Engineer – ADI – Newbury, UK

Be ready for the next coming quiz!

OK  it's time to publish the official (and right) solution! There are well real solutions for these equations!

From the second equation we can write a = 3/b

Injecting it in the first equation: 9/b² ‐ b² = 9

Or 9 ‐b4 = 9b² or b4 + 9b² ‐ 9 = 0 Let’s pose b²=y

We have then y² + 9y – 9 = 0

And hence y = [‐9 +/‐ (81 +36)1/2]/2 = [‐9+/‐1171/2]/2

Or y = 0.908 and ‐9.908

Since y = b² must be positive, the only value for y is 0.908

Therefore b = +/‐ 0.9531 and a = 3/b = +/‐ 3.1476

There are 2 sets of possible solutions:

Values for a, b are thus :

‐3.1476 and ‐0.9531

And +3.1476 and +0.9531

Big applause to our 4 first winners:

1. Gaetano PIARINO, Key Account Manager - ADI - Milan, Italy

2. Ricardo HABRE, Field Application Engineer - ADI - Farmington (MI), USA

3. Mark CEE, Senior Engineer, Systems Integration Engineering – ADI – Cavite, Philippines

4. Martin WALKER, Product Marketing Lead Engineer – ADI – Newbury, UK

Be ready for the next coming quiz!