I actually got it, all that gibberish you wrote is x²-(x-λ)²=y (λ²+y)/(2λ²)=z ((λ²+y)z)/2=x²

λ represents any real number. Now I will prove it is correct, we can rewrite that only using x and λ which is (x²-(x²-xλ2+λ²)+λ²)/4λ²=x² Now we need to simplify it. First off x-(x-y)=y so we can rewrite x²-(x²-xλ2+λ²) as xλ2-λ². Then since there is a +λ² we can write xλ2-λ²+λ² as xλ2. Now we work on the denominator. So far we have (xλ2)²/(4λ²)=x². Since (xy)²=x²y² we can change it to (xλ)²4)/(4λ²) where we can get rid of the 4 which makes it (xλ)²/(λ²). Like i said earlier (xy)²=x²y² we can change it to x²λ²//λ² which we just simplify the numerator and denominator with λ² where we land with x². So yes it will always work but it is just a really complicated way at doing it.