Algebra
Calculus
Trigonometry
Matrix
Question
Find the roots
a1=0,a2=1
Evaluate
a3−a
To find the roots of the expression,set the expression equal to 0
a3−a=0
Rewrite the expression
a3−a=0
Separate the equation into 2 possible cases
a3−a=0,a3≥0−a3−a=0,a3<0
Solve the equation
More Steps
Evaluate
a3−a=0
Factor the expression
a(a2−1)=0
Separate the equation into 2 possible cases
a=0a2−1=0
Solve the equation
More Steps
Evaluate
a2−1=0
Move the constant to the right-hand side and change its sign
a2=0+1
Removing 0 doesn't change the value,so remove it from the expression
a2=1
Take the root of both sides of the equation and remember to use both positive and negative roots
a=±1
Simplify the expression
a=±1
Separate the equation into 2 possible cases
a=1a=−1
a=0a=1a=−1
a=0a=1a=−1,a3≥0−a3−a=0,a3<0
The only way a base raised to an odd power can be greater than or equal to 0 is if the base is greater than or equal to 0
a=0a=1a=−1,a≥0−a3−a=0,a3<0
Solve the equation
More Steps
Evaluate
−a3−a=0
Factor the expression
−a(a2+1)=0
Divide both sides
a(a2+1)=0
Separate the equation into 2 possible cases
a=0a2+1=0
Solve the equation
More Steps
Evaluate
a2+1=0
Move the constant to the right-hand side and change its sign
a2=0−1
Removing 0 doesn't change the value,so remove it from the expression
a2=−1
Take the root of both sides of the equation and remember to use both positive and negative roots
a=±−1
Simplify the expression
a=±i
Separate the equation into 2 possible cases
a=ia=−i
a=0a=ia=−i
a=0a=1a=−1,a≥0a=0a=ia=−i,a3<0
The only way a base raised to an odd power can be less than 0 is if the base is less than 0
a=0a=1a=−1,a≥0a=0a=ia=−i,a<0
Find the intersection
a=0a=1a=0a=ia=−i,a<0
Find the intersection
a=0a=1a∈∅
Find the union
a=0a=1
Solution
a1=0,a2=1
Show Solution
