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3 years ago

A number multiplied by 12 is equal to the sum of the square root of that same number and 36. What is that number?

Mathematics

1 answer:

Pavlova-9 [17]3 years ago

7 0

Answer:

3.15

Step-by-step explanation:

Let the unknown number be n.

Then 12n = √n + 36

We must eliminate the √ operator. One way to do this is to replace √n temporarily with x. Then 12n = 12x^2, and we have 12x^2 - x - 36 = 0. This is a quadratic with a= 12, b= -1 and c = -36

Solving for x using the quadratic formula:

1 plus or minus √(1 - 4(12)(-36)

x = ----------------------------------------------

2(12)

1 plus or minus √1729

x = -----------------------------------

1 plus or minus 41.58

x = -----------------------------------

Since x = √n, n must be a positive number. Thus,

1 + 41.58

x = ---------------- = 1.77

If x = 1.77 = √n, then n = 1.77^2 = 3.15.

Check: Is this true? A number multiplied by 12 is equal to the sum of the square root of that same number and 36.

12(3.15) = √3.15 + 36, or

37.8 = 1.77 + 36 = 37.77 This checks out.

The number is 3.15

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Step-by-step explanation:

Given:

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$\dfrac{2a^2-4a+2}{3a^2-3}=\dfrac{2(x-1)}{3(x+1)}$

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