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Find 2 consecutive numbers whose squares differ by 25.

User Tarun
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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.

User Zedfoxus
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