9514 1404 393
Answer:
x = -1
Step-by-step explanation:
A graphical solution can avoid extraneous solutions. The attachment shows the one solution is x = -1.
__
Squaring both sides gives ...
x +5 = (x +3)² = x² +6x +9
Putting this in standard form, we have ...
x² +5x +4 = 0
(x +1)(x +4) = 0 . . . . . factor
x = -1 or -4 . . . . . . . . values of x that make the factors zero
__
Since we require the root to be non-negative, we must have ...
x +3 ≥ 0
x ≥ -3
The only solution that satisfies this requirement is x = -1. The solution x = -4 is extraneous. The solution is x = -1.
Answer:
The sum of the two numbers is 15
Step-by-step explanation:
Let the counting numbers be x and y.
Then we can write the following equations
x=4y.......1 (one is four times greater )
x(y)=36.....2 (the product of the two)
Putting equation 1 into equation 2, we get
4y(y)=36
Dividing through by 4,we get
Taking square root of both side, we obtain
y=3
Putting the value of y into equation , we get
x=4(3)=12
Hence the numbers are 3 and 12
Therefore the sum of the two numbers is 3+12=15
