Example.1
If y +
1/y = -2 then find the value of y200 + 
.
Solution
y + 1/y =
-2
= -2
y2 + 1 + 2y = 0
(y + 1)2 = 0
y + 1 = 0 \ y = -1
\ y200 = (-1)even
= 1. \ y200 = = 2.
example.2
If 4x – 
= 20, then find the value of 5x – 
.
Solution
4x – = 20
Multiplying both sides by 
we get, 5x – = 25.
example.3
If y3 - 3y2 + 3y = 28
then find the value of y. .
Solution
Given y3 - 3y2 + 3y =
28. Subtracting 1 on both sides, .
y3 – 3y2 + 3y - 1 = 27
(y - 1)3 = 27 (… a3 -
3a2b + 3ab2 - b3 = (a - b)3)
&⇒ y - 1 = 3
&⇒ y = 4. .
example.4
If a
– b+ c= 0, then 
is equal to
Solution
When p + q + r = 0, p3 + q3
+ r3 = 3pqr
\ If a– b+ c= 0 i.e. a+(-b)+ c= 0,
i.e. a - b + c = 3 (a(- b) (c))1/3
= - 3 (abc)1/3 .
Cubing on both sides, (a - b + c)3
= - 27(abc)
= -27.
example.5
If x = 38, y = -27, z = -11 then find the
value of x3 + y3 + z3 - 3 x y z. .
Solution
Given that: x = 38, y = - 27 and z = -11
&⇒ x + y + z = 38 - 27 – 11 = 0
&⇒ x + y + z = 0
&⇒ (x3 + y3 +
z3 - 3 x y z) = 0. .
