Question 455232: Twice the sum of two numbers is 28. The sum of the squares of the two numbers is 100. What is the product of the two numbers?
Answer by mathmartian(7)   (Show Source):
You can put this solution on YOUR website! Let's begin by using the variables x and y to represent the two numbers.
Next, let's write two algebraic equations to represent the problem.
For twice the sum of two numbers is 28, we can write 2(x+y)=28
For the sum of the squares of the two numbers is 100, we can write x²+y²=100
The problem wants us to solve for the product of the two numbers, or xy.
Now notice that the key to solving this problem involves squaring equations.
To simplify, divide both sides of the first equations by 2, to get x+y=14
Now square this equation. (x+y)²=14²
Simplify, and you get x²+2xy+y²=196
See the link yet?
Well, let's substitute the equation x²+y²=100 into this equation.
100+2xy=196
Now subtract 100 from both sides, 2xy=96
Lastly, divide both sides by 2, and you get your answer, xy=48
Great job. Keep it up!
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