Answer:
[tex] \boxed{x - y = -2\sqrt{7}} [/tex]
Given:
[tex]x + y = 4 \\ \\ {x}^{2} + {y}^{2} = 22 \\ \\ {x}^{4} = {y}^{4} - 176 \sqrt{7} [/tex]
Step-by-step explanation:
[tex] = > {x}^{4} = {y}^{4} - 176 \sqrt{7} \\ \\ = > {x}^{4} - {y}^{4} = - 176 \sqrt{7} \\ \\ = > {( {x}^{2}) }^{2} - { ({y}^{2}) }^{2} = - 176 \sqrt{7} \\ \\ = > ( {x}^{2} + {y}^{2} )( {x}^{2} - {y}^{2} ) = - 176 \sqrt{7} \\ \\ = > ( {x}^{2} + {y}^{2}) (x + y)(x - y) = - 176 \sqrt{?} \\ \\ = > 22 \times 4(x - y) = - 176 \sqrt{7} \\ \\ = > 88(x - y) = - 176 \sqrt{7} \\ \\ = > x - y = - \frac{176 \sqrt{7} }{88} \\ \\ = > x - y = - 2 \sqrt{7} [/tex]
Identity used:
[tex]{x}^{2} - {y}^{2} = (x + y)(x - y)[/tex]
