The sum of two numbers is 2 and their difference is 1. what is their product?

Question

how do you solve that?

Answer 1

[11]
Let the numbers be a and b
a+b=2
a-b=1
We know that
4ab=(a+b)^2-(a-b)^2
=2^2-1^2
=4-1=3
Therefore ab=3/4
Therefore,the product of the numbers is 3/4

Answer 2

Let x and y be the two numbers
x + y = 2 >>> y = 2 - x
| x - y | = 1
| x - (2 - x) | = 1
| x - 2 + x | = 1
| 2x - 2 | = 1
2x - 2 = 1 or 2x - 2 = -1
x = 3/2 or 1/2
when x = 3/2, y = 1/2, xy = 3/4
when x = 1/2, y = 3/2, xy = 3/4
Hence, their product is 3/4.

Answer 3

x + y = 2
x - y = 1

2x = 3

x = 3/2

y = 1/2

3/2*1/2 = 3/4 is the product.

Answer 4

a + b = 2
a - b = 1

Here's a tricky way where you don't even need to figure out a and b:

(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²

If you subtract the two you'll get 4ab, then divide by 4.

2² - 1² = 4ab
3 = 4ab

ab = 3/4

Answer 5

x + y = 2
x - y = 1
2x = 3
x = 1.5
y = .5
xy= .75

Answer 6

0.75