Question
Solve the inequality
Solve for b
Solve for c
b≥ac320ac2,c>0b≤ac320ac2,c<0
Evaluate
a2b3c≥20
Rewrite the expression
a2cb3≥20
Divide both sides
a2ca2cb3≥a2c20
Divide the numbers
b3≥a2c20
Rewrite the inequalities
{b3≥a2c20c>0{b3≤a2c20c<0
Calculate
More Steps

Calculate
b3≥a2c20
Take the 3-th root on both sides of the equation
3b3≥3a2c20
Calculate
b≥3a2c20
Simplify the root
More Steps

Evaluate
3a2c20
To take a root of a fraction,take the root of the numerator and denominator separately
3a2c320
Multiply by the Conjugate
3a2c×3ac2320×3ac2
Calculate
ac320×3ac2
The product of roots with the same index is equal to the root of the product
ac320ac2
b≥ac320ac2
{b≥ac320ac2c>0{b3≤a2c20c<0
Calculate
More Steps

Calculate
b3≤a2c20
Take the 3-th root on both sides of the equation
3b3≤3a2c20
Calculate
b≤3a2c20
Simplify the root
More Steps

Evaluate
3a2c20
To take a root of a fraction,take the root of the numerator and denominator separately
3a2c320
Multiply by the Conjugate
3a2c×3ac2320×3ac2
Calculate
ac320×3ac2
The product of roots with the same index is equal to the root of the product
ac320ac2
b≤ac320ac2
{b≥ac320ac2c>0{b≤ac320ac2c<0
Solution
b≥ac320ac2,c>0b≤ac320ac2,c<0
Show Solution
