Final answer:
To find two consecutive numbers whose squares differ by 25, we can set up an equation and solve for x. The two consecutive numbers are -25.5 and -24.5.
Step-by-step explanation:
To find two consecutive numbers whose squares differ by 25, we can set up an equation.
Let's assume the two consecutive numbers are x and x+1.
Their squares would be x^2 and (x+1)^2.
We can set up the equation x^2 - (x+1)^2 = 25 and solve for x.
Expanding (x+1)^2, we get x^2 + 2x + 1.
Substituting this into the equation, we have x^2 - (x^2 + 2x + 1) = 25.
Simplifying, we get -2x - 26 = 25.
Adding 26 to both sides, we have -2x = 51.
Dividing both sides by -2, we get x = -25.5.
So the two consecutive numbers are -25.5 and -24.5.