Divide
1. (i) x*5 = x³
Answers
x=25
Step-by-step explanation:
x*5=x³
x³/x=5
5=x²
x=5²
x=25
Answer:
0
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
x*5-(x^3)=0
Step by step solution :
STEP
1
:
STEP
2
:
Pulling out like terms
2.1 Pull out like factors :
5x - x3 = -x • (x2 - 5)
Trying to factor as a Difference of Squares:
2.2 Factoring: x2 - 5
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 5 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares.
Equation at the end of step
2
:
-x • (x2 - 5) = 0
STEP
3
:
Theory - Roots of a product
3.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:
3.2 Solve : -x = 0
Multiply both sides of the equation by (-1) : x = 0
Solving a Single Variable Equation:
3.3 Solve : x2-5 = 0
Add 5 to both sides of the equation :
x2 = 5
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
x = ± √ 5
The equation has two real solutions
These solutions are x = ± √5 = ± 2.2361
Three solutions were found :
x = ± √5 = ± 2.2361
x = 0