Question

Need help with a system of equations

Answer 1

-2
`√(7)`

Explanation:

`x^(4) - y^(4) = -176√(7) \\(x^(2) + y^(2))(x^(2) - y^(2) ) = -176√(7) \\(x^(2) - y^(2) )= (-176√(7))/(22) \\(x + y)(x - y) = -8√(7)\\ x - y = (-8√(7))/(4) = -2√(7)`

Answer 2

`\boxed{x - y = -2√(7)}`

Given:

`x + y = 4 \\ \\ {x}^(2) + {y}^(2) = 22 \\ \\ {x}^(4) = {y}^(4) - 176 √(7)`

Explanation:

`= > {x}^(4) = {y}^(4) - 176 √(7) \\ \\ = > {x}^(4) - {y}^(4) = - 176 √(7) \\ \\ = > {( {x}^(2)) }^(2) - { ({y}^(2)) }^(2) = - 176 √(7) \\ \\ = > ( {x}^(2) + {y}^(2) )( {x}^(2) - {y}^(2) ) = - 176 √(7) \\ \\ = > ( {x}^(2) + {y}^(2)) (x + y)(x - y) = - 176 √(?) \\ \\ = > 22 * 4(x - y) = - 176 √(7) \\ \\ = > 88(x - y) = - 176 √(7) \\ \\ = > x - y = - (176 √(7) )/(88) \\ \\ = > x - y = - 2 √(7)`

Identity used:

`{x}^(2) - {y}^(2) = (x + y)(x - y)`