Question

Write an equation of the form x2 = r

where r is a real number that has exactly
one real solution.

Answer 1

An equation x² = r that has exactly one real solution is x² = 0. The only real solution to this equation is x = 0, as only 0 squared equals 0.

Step-by-step explanation:

To write an equation of the form x² = r with exactly one real solution, we need to choose a value for r such that when we take the square root of both sides of the equation, we only get one solution. The only value for r that satisfies this condition is 0 because the square root of 0 is 0, and there are not two different numbers that when squared would produce 0.

Hence, an equation that meets the requirements is:

x² = 0

The unique solution to this equation is x = 0. This is because when we apply the square root to both sides, √(x²) = √(0), we end up with x = 0. Only 0 squared returns 0, so there cannot be another solution.