The sum of two numbers is 22 and the sum of their squares is 404 . the product of two numbers is-
Created: 2 years ago |
Updated: 7 months ago
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Let's denote the two numbers as x and y.
According to the given information, we have two equations:
- x + y = 22 (the sum of two numbers is 22).
- x^2 + y^2 = 404 (the sum of their squares is 404).
Now, let's find the product of the two numbers, which is xy.
We can use the following identity: (x + y)^2 = x^2 + 2xy + y^2
We already know that x + y = 22, and we know x^2 + y^2 = 404.
So, we can rewrite the identity as: (22)^2 = x^2 + 2xy + 404
484 = x^2 + 2xy + 404
Now, let's isolate 2xy: 2xy = 484 - 404 2xy = 80
Now, divide both sides by 2 to find the product xy: xy = 80 / 2 xy = 40
So, the product of the two numbers x and y is 40. The correct answer is 40.
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