Basic Algebra Equation Solution! Equation Solving Method.

Q.NO. 01: What are the values of x in the equation x³ - 5x² - x + 5 = 0? 

Solution:

In order to solve this equation,  Apply factorization:

(x^3 - 5x^2) + (-x + 5) = 0

Taking common from above brackets:

x^2 (x - 5) -1 (x - 5) = 0

(x - 5) (x^2 - 1) = 0

For values of "X"

x^2 - 1 = 0

x^2 = 1

Taking square root on both sides:

x = +1

x = -1

Or

x - 5 = 0

x = 5

Solution Set : { +1, -1, +5}

Q.NO.02: If x+1/x=3, then what is the value of x³+1/x³=?

Solution:

Given:

X + 1/X = 3

X^3 + 1/X^3 = ?

Solution:

As we know:

( X + 1/X)^3 = X^3 + 1/X^3 + 3(X)(1/X) (X + 1/X)

In above equation (x) will be cancel with (1/X)

( X + 1/X)^3 = X^3 + 1/X^3 + 3(X + 1/X)

Put the values

( 3)^3 = X^3 + 1/X^3 + 3(3)

27 = X^3 + 1/X^3 + 9

X^3 + 1/X^3 = 27 - 9

X^3 + 1/X^3 = 18

Q.NO.03: If f(x) = 2x² - 5x + 3, what is the value of f (x + 1)?

Solution:

For solving this equation, Replace X with X + 1

f(X + 1) = 2(X + 1)^2 - 5(X + 1) + 3

Open (X + 1)^2 with (a+b) whole square formula:

f(X + 1) = 2(X^2 +2X + 1) - 5(X + 1) + 3

Multiply the value of 5 and 2 with its respective brackets:

f(X + 1) = 2X^2 +4X + 2 - 5X - 5 + 3

f(X + 1) = 2X^2 - X

f(X + 1) = X (2X - 1)