Create an equation where the left side is a linear function and the right side is a square root function. Make it so that the equation has exactly two solutions.

Start with what I gave you here:

http://www.jiskha.com/display.cgi?id=1483383485

Pick any two points on y = ?x
e.g. (9,3) and some other point

find the equation of the straight line passing through two points, and you are done

Thank you Reiny for helping I was having trouble solving these problems.

(x+1)^3 = ∛(x^2)

To create an equation with a linear function on the left side and a square root function on the right side, we can set up an equation in the form:

ax + b = √(cx + d)

Where a, b, c, and d are constants.

To ensure that the equation has exactly two solutions, we need to consider the properties of square root functions. One important property is that the square root of a number (or expression) is always positive or zero. Therefore, for the equation to have two solutions, one possibility is that the expression inside the square root must be zero. Let's construct an equation using this idea:

Start with a linear function on the left side, such as:

x + 5

Set it equal to the square root function with expression zero on the right side, like this:

x + 5 = √(0x + 0)

Simplifying the right side of the equation:

x + 5 = √0

Since the square root of zero (√0) is zero, our equation becomes:

x + 5 = 0

Now, let's solve this equation to find the values of x:

x = -5

Thus, we have obtained one solution for x, which is -5. But we need another solution to fulfill the requirement of having exactly two solutions. To achieve this, we can modify the equation:

(x + 5)^2 = √(0x + 0)

By squaring both sides, the equation becomes:

x^2 + 10x + 25 = 0

Now, we can solve this quadratic equation to find the second solution of x:

Using factoring or the quadratic formula, we can find that the solutions are:

x = -5 (repeated solution)

Therefore, the equation x^2 + 10x + 25 = 0 fulfills the requirement of having exactly two solutions while having a linear function on the left side and a square root function on the right side.