Posted on - 05-02-2017

Bank PO

In arithmetic we express 1+ 1+ 1= 3, 2 x 2 x 2 = 8, 3 – 2 = 1 etc., Here 1, 2, 3, 8 are known numbers. In algebra we deal with symbols like x, y, z, a, b, c, p etc., which represent unknown numbers. .

x + x + x = 3x, a x a x a = a^{3},
3x - 2x = x are some examples of algebraic statements. In the above examples 1,
2, 3 and 8 are known and x, y, z, c, b, c and p are unknowns. .

When x + y = 10, the value of x depends on the value of y and vice-versa. Here 10 is a constant and x, y are variables. .

We can define algebra as a branch of mathematics which deals with rules, procedures and operations involving wns and unknowns; and constants and variables.

Algebraic expressions are formed from variables and constants. 3x + 4y is an algebraic expression. The value of an expression depends on the values of the variables from which the expression is formed. .

Formulas in algebra are written in a general form using algebraic expressions. .

The following algebraic formulas should be memorized since they are very useful to solve certain problems. .

(a + b)^{2} = a^{2} + 2ab +
b^{2}

(a - b)^{2} = a^{2} - 2ab +
b^{2}

(a + b)^{2} = a^{2} + b^{2}
+ c^{2} + 2ab + 2bc + 2ca

(a + b)^{3} = a^{3} + b^{3}
+ 3ab (a + b)

(a - b)^{3} = a^{3} – b^{3}
- 3ab (a - b)

a^{3} + b^{3} = (a + b) (a^{2}
- ab + b^{2})

a^{3} - b^{3} = (a - b) (a^{2}
+ ab + b^{2})

a^{3} + b^{3} + c^{3}
- 3abc = (a + b + c) (a^{2 }+ b^{2} + c^{2} - ab - bc -
ca)

if a + b + c = 0, then a^{3} + b^{3}
+ c^{3} = 3abc. .

If a = 13, b = 12, then find the value of

Given that a = 13, b = 12. .

= a + b

= = a + b

= 13 + 12 = 25

x = 103, then find the value of

.

= =

(\ a^{3} - 3ba^{2} + 3ab^{2} – b^{3}
= (a - b)^{3})

= x - 2 = 101

If y + = 10, then find the value of .

y + = 10

Multiplying by y on both sides,

y^{2} + 25 = 10y

y^{2} - 10y + 25 = 0

(y - 5)^{2} = 0

y - 5 = 0

y = 5

.

If 3y + = 3,
then find the value of 64y^{3 }+ .

3y + = 3

Multiplying both sides by 4y + = 4.

Cubing on both sides,

64y^{3} + + 3(4y)= 64

(\ (a + b)^{3} = a^{3} + b^{3} + 3ab (a +
b))

64y^{3} + + 4 (4)
= 64

64y^{3 }+ = 48

If y + , then find the value of

x =