## Example.1

If y +
1/y = -2 then find the value of y^{200} + .

### Solution

y + 1/y =
-2

= -2

y^{2} + 1 + 2y = 0

(y + 1)^{2} = 0

y + 1 = 0 \ y = -1

\ y^{200} = (-1)^{even}
= 1. \ y^{200} = = 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 y^{3} - 3y^{2} + 3y = 28
then find the value of y. .

### Solution

Given y^{3} - 3y^{2} + 3y =
28. Subtracting 1 on both sides, .

y^{3} – 3y^{2} + 3y - 1 = 27

(y - 1)^{3} = 27 (… a^{3} -
3a^{2}b + 3ab^{2} - b^{3} = (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, p^{3} + q^{3}
+ r^{3} = 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 x^{3} + y^{3} + z^{3} - 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

&⇒ (x^{3} + y^{3} +
z^{3} - 3 x y z) = 0. .