Question
Solve the inequality
a∈/R
Alternative Form
No real solution
Evaluate
0<a<a1<a2
Separate into two inequalities
⎩⎨⎧0<aa<a×1a×1<a2
Swap the sides of the inequality
⎩⎨⎧a>0a<a×1a×1<a2
Solve the inequality
More Steps

Evaluate
a<a×1
Any expression multiplied by 1 remains the same
a<a
The statement is false for any value of a
a∈/R
⎩⎨⎧a>0a∈/Ra×1<a2
Solve the inequality
More Steps

Evaluate
a×1<a2
Any expression multiplied by 1 remains the same
a<a2
Move the expression to the left side
a−a2<0
Evaluate
a2−a>0
Add the same value to both sides
a2−a+41>41
Evaluate
(a−21)2>41
Take the 2-th root on both sides of the inequality
(a−21)2>41
Calculate
a−21>21
Separate the inequality into 2 possible cases
a−21>21a−21<−21
Calculate
More Steps

Evaluate
a−21>21
Move the constant to the right side
a>21+21
Add the numbers
a>1
a>1a−21<−21
Cancel equal terms on both sides of the expression
a>1a<0
Find the union
a∈(−∞,0)∪(1,+∞)
⎩⎨⎧a>0a∈/Ra∈(−∞,0)∪(1,+∞)
Solution
a∈/R
Alternative Form
No real solution
Show Solution
