Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2007 | January | Q#3

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Question

a.  Express  in the form of , where  and  are integers.

b.  

                   i.       Express  in the form  , where n is an integer.

                  ii.       Solve the equation

giving your answer in its simplest form.

Solution

a.
 

We are given;

 

If we need a rational number in the denominator of a fraction, we need to follow procedure of  “denominator rationalization” as given below.

ü If the denominator is of the form  then multiply both numerator and denominator by .

ü If the denominator is of the form  then multiply both numerator and denominator by  .

ü If the denominator is of the form  then multiply both numerator and denominator by .

  We have algebraic formula;

Utilizing this on the denominator, we get;

We can expand by multiplication as;

b.
 

Since ;

Comparing with  gives us;

c.
 

Since ;

Since ;

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