difference is 7, product is 30
it sucks
3 and 10
a * b = 30 .....1
a - b = 7 ..... 2
a = 7 + b ......3
(7+b)(b)=30
b^2+7b-30=0
(using quadratic formula)
b = -10 or b = 3
a = -3 or a = 10
To find the two numbers given the difference and product, we can set up a system of equations. Let's call the two numbers x and y.
1) Since the difference between the two numbers is 7, we can write the equation: x - y = 7.
2) Since the product of the two numbers is 30, we can write the equation: xy = 30.
Now we have a system of equations:
Equation 1: x - y = 7
Equation 2: xy = 30
To solve this system, we can use the substitution method or elimination method. Let's use the substitution method:
From Equation 1, we can isolate x as follows:
x = 7 + y
Now substitute this value of x into Equation 2:
(7 + y)y = 30
Expanding the equation, we have:
7y + y^2 = 30
Rearranging the equation:
y^2 + 7y - 30 = 0
Now we can factorize this quadratic equation:
(y + 10)(y - 3) = 0
Setting each factor to zero, we get two possible values for y:
y + 10 = 0 --> y = -10
or
y - 3 = 0 --> y = 3
Now substitute these values back into Equation 1 to find the corresponding values of x:
If y = -10:
x = 7 + (-10) --> x = -3
If y = 3:
x = 7 + 3 --> x = 10
Therefore, the two numbers are either (-3, -10) or (10, 3).