- In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
- $$f ( x ) = ( x + \sqrt { 2 } ) ^ { 2 } + ( 3 x - 5 \sqrt { 8 } ) ^ { 2 }$$
Express \(\mathrm { f } ( x )\) in the form \(a x ^ { 2 } + b x \sqrt { 2 } + c\) where \(a , b\) and \(c\) are integers to be found.
- Solve the equation
$$\sqrt { 3 } ( 4 y - 3 \sqrt { 3 } ) = 5 y + \sqrt { 3 }$$
giving your answer in the form \(p + q \sqrt { 3 }\) where \(p\) and \(q\) are simplified fractions to be found.