Question

If you answer yo get 20 points

When the square of a number is increased by one, the result is four times the original

number. Find the number.​

Answer 1

3.732 or 0.268 to the nearest thousandth.

Exact values are 2 + √12/2 or 2 - √12/2.

Explanation:

Let the original number be x, then:

x^2 + 1 = 4x

x^2 - 4x + 1 = 0

x = [-(-4) +/- sqrt(16 - 4*1*1]) / 2

x = (4 + sqrt12)/ 2 , (4 - sqrt12) / 2

= 3.732, 0.268.

Answer 2

n = 2 + 2√3 and n = 2 - 2√3

Explanation:

Let the number be n.

Then n² + 1 = 4n.

Rearranging this in proper quadratic format:

n² - 4n + 1

Here the coefficients are a = 1, b = -4 and c = 1.

Then the discriminant is b²-4ac, or (-4)²-4(1)(1) ), or 16 - 4, or 12.

By applying the quadratic formula, we find that the roots are:

- (-4) ± √12

n = ------------------

2

or n = 2 + 2√3 and n = 2 - 2√3