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# Assignment 1

Hi,

I'm stuck on the last part of the step question where they ask you to show that c^2 is between 1 and 0, but one of the equations they gave us shows that c^2 is negative. I read the hints where they told us to use the first equation given which involves c^2. However, it is that same equation which shows that c^2 is negative.

Help pleas

### How exactly does it show that

How exactly does it show that $c^2$ is negative? Do you mean because of the negative sign? If so, what happens if one of $a$ and $b$ is negative? Remember that $-(-1) = +1$.

Instead, you're given that $c$ is a real number, from which you can immediately deduce that $c^2 \geq 0$. It's up to you to show that $c^2 \neq 0$ (hint: contradiction) that immediately tells you that $c^2 > 0$.

## Useful Links

Underground Mathematics: Selected worked STEP questions

STEP Question database

University of Cambridge Mathematics Faculty: What do we look for?

University of Cambridge Mathematics Faculty: Information about STEP

University of Cambridge Admissions Office: Undergraduate course information for Mathematics

Stephen Siklos' "Advanced Problems in Mathematics" book (external link)

MEI: Worked solutions to STEP questions (external link)

OCR: Exam board information about STEP (external link)

AMSP (Advanced Maths Support programme): Support for University Admission Tests (external link)