<s>[INST] The value of $a+b=ab=a^2-b^2$ If $a+b=ab=a^2-b^2$ and $a$ and $b$ are real numbers then what do all of the expressions evaluate to?


*

*$(1+\sqrt5)/2$

*$(3+\sqrt5)/2$

*2

*$\sqrt5$


Not sure at all how to find the answer. I tried $a=ab/b$ and $a=(a^2-b^2)/b$ but after that I am lost.
 [/INST] Any time you see $a^2-b^2$ you should think $(a+b)(a-b)$.  Here if $a+b \neq 0$ you can divide it out to get $1=a-b$  Then $a=b+1, a+b=2b+1=(b+1)b$ and feed it to the quadratic formula.  
If $a+b=0$ we must have $a=b=0$ and the sum is again $0$, which should have been one of the choices.
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