Question

Ayuda porfavor todo desarrolo

Answer 1

PROBLEMA 2

[tex]x + y = 3 \sqrt{xy} [/tex]

[tex](x + y) {}^{2} = {x}^{2} + {y}^{2} + 2xy \\ (3 \sqrt{xy} ) {}^{2} = {x}^{2} + {y}^{2} + 2xy \\ 9xy = {x}^{2} + {y}^{2} + 2xy \\ 9xy - 2xy = {x}^{2} + {y}^{2} \\ 7xy = {x}^{2} + {y}^{2} [/tex]

[tex]xy( \frac{1}{ {x}^{2} } + \frac{1}{ {y}^{2} } ) \\ xy( \frac{ {x}^{2} + {y}^{2} }{ {x}^{2} {y}^{2} } ) \\ \frac{ {x}^{2} + {y}^{2} }{xy} \\ \frac{7xy}{xy} \\ 7[/tex]

PROBLEMA 6

[tex](x + y) {}^{2} = {x}^{2} + {y}^{2} + 2xy \\ ( \sqrt[3]{2} ) {}^{2} = {x}^{2} + {y}^{2} + 2( \sqrt[3]{4} ) \\ \sqrt[3]{4} = {x}^{2} + {y}^{2} + 2 \sqrt[3]{4} \\ \sqrt[3]{4} - 2 \sqrt[3]{4} = {x}^{2} + {y}^{2} \\ - \sqrt[3]{4} = {x}^{2} + {y}^{2} [/tex]

[tex]T = (x + y) {}^{2} ( {x}^{2} - xy + {y}^{2} ) {}^{2} - 4 {x}^{3} {y}^{3} \\ T = ( \sqrt[3]{2} ) {}^{2} ( - \sqrt[3]{4} - \sqrt[3]{4} ) {}^{2} - 4( \sqrt[3]{4} ) {}^{3} \\ T = (\sqrt[3]{4} )( - 2 \sqrt[3]{4} ) {}^{2} - 4(4) \\ T = ( \sqrt[3]{4} )(8 \sqrt[3]{2} ) - 16 \\ T = 16 - 16 \\ T = 0[/tex]

PROBLEMA 3

[tex]x + y + z = 0[/tex]

[tex] {x}^{3} + {y}^{3} + {z}^{3} = 3xyz[/tex]

[tex]M = \frac{ {x}^{3} + {y}^{3} + {z}^{3} }{9xyz} \\ M = \frac{3xyz}{9xyz} \\ M = \frac{1}{3} [/tex]