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The sum of an integer and its square root is 12. Find the integer.

User Brad Lanam
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1 Answer

7 votes

Answer:

9

Explanation:

Let's call the integer "x." According to the information given, the sum of the integer and its square root is 12. This can be written as an equation:

x + √x = 12

Now, we need to solve for x. To do this, we'll first isolate the square root term:

√x = 12 - x

Now, square both sides to get rid of the square root:

x = (12 - x)^2

x = (12 - x)(12 - x)

x = 144 - 24x + x^2

Now, rearrange the terms and set the equation equal to zero:

x^2 - 25x + 144 = 0

Now, you can factor this equation:

(x - 16)(x - 9) = 0

This gives you two possible solutions for x:

x - 16 = 0, so x = 16

x - 9 = 0, so x = 9

So, there are two possible integers, x = 16 and x = 9, that satisfy the given condition.

User Samuel Audet
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