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In 1991, the population of Melonville was a square number. In 1992, with an increase of 100, the population became 1 greater than a perfect square. In 1993, with another increase of 100, the population again became a perfect square. Find the population of Melonville in 1993.

Sagot :

MrRoyal

The population of Melonville follows a population growth, and the population of Melonville in 1993 is 201

How to determine the population?

Let the population in 1991 be x².

The 1992 population is

P₂ = y² + 1 = x² + 100

This means that:

x² + 100 = y² + 1

Rewrite as:

y² - x² = 100 - 1

y² - x² = 99

Express as difference of two squares

(y - x)(y + x) = 99

Express 99 as 9 * 11

(y - x)(y + x) = 9 * 11

Rewrite as:

(y - x)(y + x) = (10 - 1) * (10 + 1)

By comparison, we have:

y = 10 and x = 1

So, the populations are:

P₁ = x² --- 1991

P₂ = x² + 100 --- 1992

P₃ = x² +100 +100 --- 1993

Substitute 1 for x

P₃ = 1² +100 +100

Evaluate

P₃ = 201

Hence, the population of Melonville in 1993 is 201

Read more about population growth at:

https://brainly.com/question/20115298

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