FP1 Alpha Beta roots

I am highly surely I have done this question before with ease, but after coming back to it now I am struggling to make the jump from a+b and ab to what they write as a/b + b/a?

1. $\frac{\alpha}{\beta}+\frac{\beta}{\alpha} = \frac{\alpha^2+\beta^2}{\alpha \beta}$

2. $(\alpha+\beta)^2 = \alpha^2+2\alpha\beta+\beta^2$

step 2 is incorrect as a^2+b^2 does not equal (a+b)^2.

It helps to remember these:

a^2+b^2 = (a+b)^2-2(ab)

a^3+b^3 = (a+b)^3-3(ab)(a+b)

step 2 is incorrect

as a^2+b^2 does not equal (a+b)^2.

It's not a step: it's a hint



That is true a.e.

Step 2 is not incorrect

There was no suggestion that $a^2+b^2 = (a+b)^2$

You use step 2 to re-write the numerator of step 1


It does not help to remember the rearrangements of standard expansions ... it is better to understand how to use them

Ofcourse it helps to remember the rearrangements, from the point of view of the original exam question it saves a lot of time. Im sure everyone can do the rearrangements but in an exam; but time has to be managed carefully