the difference of two numbers is 5. their product is 176. what are the numbers ? i've been trying to figure this out for a while and can't come out with the right answer.
thanx ms.sue it really help me solve the answer
Eq1: X - Y = 5.
Eq2: XY = 176.
Solve for Y in Eq2:
Y = 176/X,
In Eq1, substitute 176/X for Y:
X - 176/X = 5,
Multiply both sides by X:
X^2 - 176 = 5X,
X^2 - 5X - 176 = 0,
Solve using the Quadratic Formula and
get:
X = 16, and -11.
In Eq1, substitute 16 for X:
16 - Y = 5,
Y = 11.
In Eq1, substitute -11 for X:
-11 - Y = 5,
Y = -16.
Solution set: (X,Y)=(16,11),(-11,-16).
So 2 sets of numbers satisfy the required conditions.
could you give me an exact answer please I need to love this within a day
solve*
To find the two numbers, let's set up equations based on the given information.
Let's assume the larger number is x and the smaller number is y.
According to the given information, the difference of the two numbers is 5. Hence, we can write the equation:
x - y = 5 Eq.1
Also, their product is 176. Therefore:
x * y = 176 Eq.2
Now we have a system of two equations. We can solve it to find the values of x and y.
One approach to solve the system of equations is substitution. We can rearrange Eq.1 to express x in terms of y:
x = y + 5
Substituting this value of x into Eq.2, we get:
(y + 5) * y = 176
Expanding the equation gives us:
y^2 + 5y = 176
Rearranging to form a quadratic equation:
y^2 + 5y - 176 = 0
Now, we can solve this quadratic equation to find the value(s) of y. Since it doesn't seem to factor easily, let's use the quadratic formula:
y = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = 5, and c = -176. Substituting these values, we can calculate y:
y = (-5 ± √(5^2 - 4(1)(-176))) / (2(1))
y = (-5 ± √(25 + 704)) / 2
y = (-5 ± √729) / 2
Now we have two possible solutions for y:
y = (-5 + 27) / 2 or y = (-5 - 27) / 2
Simplifying:
y = 22 / 2 or y = -32 / 2
y = 11 or y = -16
Now, substitute these values back into Eq.1 or Eq.2 to solve for x. Let's use Eq.1:
For y = 11:
x - 11 = 5
x = 16
For y = -16:
x - (-16) = 5
x + 16 = 5
x = -11
Therefore, the two numbers are either 16 and 11, or -11 and -16.