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.