Solve the radical equation 400−6x3−−−−−−−−√5=4.(1 point)
Responses
x=−213−−√3
x equals negative 2 root index 3 Start Root 13 End Root
x=56−−√3
x equals root index 3 Start Root 56 End Root
x=−13−−√3
x equals negative root index 3 Start Root 13 End Root
x=4
To solve the equation, we first simplify the left side of the equation by taking the cube root of 400:
∛400 = ∛(8 * 50) = ∛8 * ∛50 = 2∛50
Now, the equation becomes:
2∛50 - 5 = 4
Next, we isolate the radical term by subtracting 5 from both sides:
2∛50 = 9
Then, we divide both sides by 2:
∛50 = 9/2
Lastly, we cube both sides of the equation to eliminate the cube root:
(∛50)^3 = (9/2)^3
50 = (9/2)^3
50 = 729/8
Multiplying both sides by 8:
400 = 729
This is not a true statement, so there are no solutions to the equation.