find two numbers whose sum is 27 and product is 182. Related: Ex 4.1 ...
Problem:
Find two numbers whose sum is 27 and product is 182.
Solution:
Let's assume the two numbers be x and y. Then we have:
Step 1: Simplify the First Equation
From the first equation, we can solve for one variable in terms of the other. For instance, we can solve for x:
Step 2: Substitute the Value of x
Now, we can substitute the value of x into the second equation and solve for y:
- xy = 182
- (27 - y)y = 182
- 27y - y^2 = 182
- y^2 - 27y + 182 = 0
- (y - 14)(y - 13) = 0
Step 3: Find the Values of x and y
From the last equation, we can see that y = 14 or y = 13. If y = 14, then x = 13. If y = 13, then x = 14. Therefore, the two numbers are:
- x = 13 and y = 14
- x = 14 and y = 13
Conclusion:
The two numbers are 13 and 14 or 14 and 13. Both pairs of numbers have a sum of 27 and a product of 182.