Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | May-Jun | (P1-9709/11) | Q#1
Question
Solve the equation , for
Solution
i.
We have the equation;
Dividing both sides of the equation by ;
We have the relation , therefore,
To solve this equation, we can substitute . Hence,
Since given interval is , for
interval can be found as follows;
Multiplying both sides of the inequality with 2;
Since ;
Hence the given interval for is
.
To solve equation for interval
,
Using calculator we can find the values of .
To find all the solutions (roots) of , we utilize the periodic/symmetry property of
.
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Periodic/Symmetry |
or |
Therefore;
For;
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Only following solutions (roots) are within the given interval ;
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Since ;
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Therefore;
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Hence, all the solutions of the equation within the interval
are;
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