Indices and Surds

2015 Oct Nov Paper 23 Q4 Solve the following simultaneous equations, giving your answers for both (x) and (y) in the form (a+b sqrt{3}), where (a) and (b) are integers.[begin{array}{r}2 x+y=9 \sqrt{3} x+2 y=5end{array}]

2014 Oct Nov Paper 21 & 22 Q9 Integers (a) and (b) are such that ((a+3 sqrt{5})^{2}+a-b sqrt{5}=51). Find the possible values of (a) and the corresponding values of (b). 2016 Oct Nov Paper 21 & 22 Q2 Without using a calculator, find the integers (a) and (b) such that (frac{a}{sqrt{3}+1}+frac{b}{sqrt{3}-1}=sqrt{3}-3). More Similar Questions 2016 … Read more

2014 May June Paper 23 Q5(i) Do not use a calculator in this question.(i) Show that ((2 sqrt{2}+4)^{2}-8(2 sqrt{2}+3)=0).

2012 Oct Nov Paper 22 Q6 (i) Given that (frac{2^{x-3}}{8^{2 y-3}}=16^{x-y}), show that (3 x+2 y=6).(ii) Given also that (frac{5^{y}}{125^{x-2}}=25), find the value of (x) and of (y).

2012 May June Paper 21/23 Q2 A cuboid has a square base of side ((2+sqrt{3}) cm) and a volume of ((16+9 sqrt{3}) cm ^{3}). Without using a calculator, find the height of the cuboid in the form ((a+b sqrt{3}) cm), where (a) and (b) are integers. 2015 May June Paper 22 Q3 Do not use … Read more