Question

a positive real number is 3 more than another. when -6 times the smaller is added to the square of the larger, the result is 29. find the numbers.

Answer 1

If x is the smaller number and y the larger, based on the given information, you can write the following equations:

y = x + 3 the larger is 3 more than the smaller

-6x + y² = 29 6 times the smaller plust the square of the larger equal to 29

In order to find the values of x and y, proceed as follow:

Replace the expression y = x + 3, into the second equation:

-6x + y² = 29

-6x + (x + 3)² = 29 expand the parenthesis

-6x + x² + 6x + 9 = 29 simplify

x² + 9 = 29 subtract 9 both sides

x² = 29 - 20

x² = 20 apply square root both sides

x = ±√20

then, the smaller number is ±√20, and the larger is:

y = x + 3

y = √20 + 3

or

y = -√20 + 3

Hence, the numbers are:

x= √20 and y = √20 + 3

or

x = -√20 and y = -√20 + 3