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STEP 2001, Math I, #4: Show that
Given that and , show that .
Hence, or otherwise, find all solutions of the equations
(i) (ii)
STEP 2003, Math II, #2: Write down a value of
in the interval that satisfies the equation
.
Hence, or otherwise, show that
Show that
.
STEP 2007, Math I, #2: (i) Given that and that (where and are acute) show,
by considering
, that .
The non-zero integers
and satisfy
.
Show that and hence determine and .
(ii) Let
, , and be positive integers such that the highest common factor of and is 1.
Show that, if
,
then there are only two possible values for
, and give in terms of in each case.
STEP 2005, Math II, #4: The positive numbers
, and satisfy . Prove that
The positive numbers
, , , , , and satisfy
, ,
Prove that
Hence show that
[Note that
is another notation for .]
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