Question

The sum of the squares of two numbers is 8 . The product of the two numbers is 4. Find the numbers.

Answer 1

To find the two numbers, we can set up a system of equations using the given information. Solving this system of equations, we find that the two numbers are 2 and 2, or -2 and -2.

Step-by-step explanation:

To solve this problem, we can use the given information to set up a system of equations. Let's assume the two numbers are x and y. From the problem, we know that

`x^2 + y^2` = 8 and xy = 4.

We can solve this system of equations by substituting the value of y from the second equation into the first equation. This gives us
`x^2 + (4/x)^2` = 8. Multiplying both sides by
`x^2` gives us
`x^4 + 16 = 8x^2`. Rearranging the equation and factoring, we get
`x^4 - 8x^2` + 16 = 0.

This equation can be factored as
`(x^2 - 4)(x^2 - 4)` = 0. Taking the square root of both sides, we find that
`x^2` = 4. Solving for x, we get x = ±2. Substituting these values back into the second equation, we find that the two numbers are 2 and 2, or -2 and -2.

Answer 2

Explain:The sum of the squares of two numbers is 8 . The product of the two numbers is 4. Find the numbers.

i hope this helps abit