Hi Mikethm, crimsontactics and
iamapebble
Question 1
Given that a and b are the roots of the
equation x^2 = x - 2,
show that a^4 = 2 - 3a
Answer
Step 1 : Subst x = a into the
equation
Since a is the root of
the equation ie x = a, so we can substitute x = a
into the
equation ie
x^2 = x - 2
a^2 = a -
2
Step 2 : To do the proofing ie use
the LHS to prove until it is equal to the RHS or use the RHS to
prove until it is equal to the LHS
LHS = a^4
= (a^2)^2
= (a-2)^2
since a^2 = a -
2
= a^2 -4a + 4
= a - 2 - 4a +
4
since a^2 = a -
2
= 2 - 3a
= RHS (Shown)
Now, you know the tricks that the
"O" level examiners used to set questions on this 4th pattern
of the quadratic equation (alpha and beta) ie first substitute x =
a into the equation, next use this result or
some re-arranging of the result in the proofing.
Thank you for your kind attention.
Regards,
ahm97sic
PS : Dear Mikethm, your answer is actually correct. It is
just that you have not presented your answer in the proper way ie
for proofing, we use the LHS to prove until it is equal to the RHS
or use the RHS to prove until it is equal to the LHS.
