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Solved Example Algebraic Expressions for For Banking and SSC

Posted on - 06-02-2017

QA Math Algebra

Bank PO

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
. .

 
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