Begin with x=3 and modify this equation by doing the same operation to each side of the equation.
Example Equations: sqrt(x+6)=3 and 2sqrt(m-3)=0
Practice makes perfect
We are asked to write two radical equations that have 3 for a solution. First, let's recall that a radical equation is an equation that has a variable in a radicand. We will deal with one equation at a time. Keep in mind that there infinitely many radical equations that have a solution of 3, so answers may vary.
First Equation
Since we are told that 3 should be the solution of our equation, we can start with the solution equation.
x=3
Now, let's modify it by doing different operations to both sides of the equation. For example, we can add 6 to both sides using the Addition Property of Equality.
x+ 6=3+ 6 ⇔ x+6=9
Next, because we want to end up with a radical equation, let's calculate the square root of each side.
sqrt(x+6)=sqrt(9) ⇔ sqrt(x+6)=3
We conclude that radical equation sqrt(x+6)=3 has 3 for a solution. To make sure, let's substitute 3 for x and see is the equation is true.
We can form the second radical equation in a similar way. This time we can choose another variable and set it equal to 3.
m=3
Next, let's subtract 3 from each side of the equation using the Subtraction Property of Equality.
m- 3=3- 3 ⇔ m-3=0
We can also take a cube root of each side.
sqrt(m-3)=sqrt(0) ⇔ sqrt(m-3)=0
Finally, we will multiply the sides of the equation by 2 using the Multiplication Property of Equality.
2sqrt(m-3)= 2* 0 ⇔ 2sqrt(m-3)=0
Again, we can check our equation by substituting 3 for m into the equation.
