Question

Radical equation √18x−9=x⁵:
a) x= −1
b) x=1
c) x=3
d) x= −3

Answer 1

To solve the radical equation √18x−9=x⁵, subtract x⁵ from both sides, square both sides, simplify, and solve for x. The correct answer is x = 3.

Step-by-step explanation:

To solve the radical equation √18x−9=x⁵, we need to isolate the radical term. Start by subtracting x⁵ from both sides of the equation: √18x−9−x⁵=0. Then, square both sides to eliminate the radical: (√18x−9)²=(x⁵)². Simplify and solve for x.

Expanding (√18x−9)² gives us 18x−36x⁵+81. Rearrange the equation to have all terms on one side: 18x−36x⁵+81=0. Next, combine like terms: -36x⁵+18x+81=0. Finally, factor the quadratic equation or use the quadratic formula to solve for x. The correct answer is x = 3.