To find the value of x³ + y³, we can use the formula for the sum of cubes: a³ + b³ = (a + b)(a² - ab + b²).
Given:
1. Six - y = 4
2. xy = 1
Let's solve the equations step by step:
From equation 1 (Six - y = 4):
1. Rearrange the equation to solve for x: x = 4 + y
Now, substitute x = 4 + y into the second equation (xy = 1):
2. (4 + y)y = 1
3. 4y + y² = 1
4. y² + 4y - 1 = 0
Using the quadratic formula to solve for y:
5. y = (-b ± √(b² - 4ac)) / 2a
where a = 1, b = 4, and c = -1
By solving the quadratic equation, you will get two values for y. Once you have the values of y, you can substitute them back into x = 4 + y to find the corresponding values of x.
Finally, calculate x³ + y³ using the values of x and y obtained. Plug the values into the formula (a³ + b³ = (a + b)(a² - ab + b²)) to find the sum of cubes x³ + y³.
