SOLUTION: find two consecutive positive integers such that the square of the first is increased by 17 equals 4 times these second a.what is the smaller number b.what is the bigger number

Algebra ->  Equations -> SOLUTION: find two consecutive positive integers such that the square of the first is increased by 17 equals 4 times these second a.what is the smaller number b.what is the bigger number      Log On


   

Question 1008644: find two consecutive positive integers such that the square of the first is increased by 17 equals 4 times these second
a.what is the smaller number
b.what is the bigger number
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
S=smaller integer=L-1; L=larger integer=S+1
.
S%5E2%2B17=4L
S%5E2%2B17=4%28S%2B1%29
S%5E2%2B17=4S%2B4
S%5E2-4S%2B13=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aS%5E2%2BbS%2Bc=0 (in our case 1S%5E2%2B-4S%2B13+=+0) has the following solutons:

S%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-4%29%5E2-4%2A1%2A13=-36.

The discriminant -36 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -36 is + or - sqrt%28+36%29+=+6.

The solution is S%5B12%5D+=+%28--4%2B-+i%2Asqrt%28+-36+%29%29%2F2%5C1+=++%28--4%2B-+i%2A6%29%2F2%5C1+

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-4%2Ax%2B13+%29

L%5E2%2B17=4S
L%5E2%2B17=4%28L-1%29%0D%0A%7B%7B%7BL%5E2%2B17=4L-4
L%5E2-4L%2B21=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aL%5E2%2BbL%2Bc=0 (in our case 1L%5E2%2B-4L%2B21+=+0) has the following solutons:

L%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-4%29%5E2-4%2A1%2A21=-68.

The discriminant -68 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -68 is + or - sqrt%28+68%29+=+8.24621125123532.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-4%2Ax%2B21+%29

.
ANSWER: There are no real number solutions,
regardless if you consider the larger or smaller
number as first.