Question

Me ayudan con este problema?

Answer 1

Respuesta:

${ctg}^{2} ( \beta ) = 5$

Explicación paso a paso:

Aplicando Pitágoras:

${(x + y)}^{2} + {(x - y)}^{2} = {( \sqrt{6xy} )}^{2} \\ {x}^{2} + 2xy + {y}^{2} + {x}^{2} - 2xy + {y}^{2} = 6xy \\ 2( {x}^{2} + {y}^{2} ) = 6xy \\ ( {x}^{2} + {y}^{2} ) = 3xy$

Piden:

${ctg}^{2} ( \beta ) = {( \frac{x + y}{x - y}) }^{2} \\ \frac{ {x}^{2} + 2xy + {y}^{2} }{ {x}^{2} - 2xy + {y}^{2} } = \frac{3xy + 2xy}{3xy - 2xy} \\ \frac{5xy}{1xy} = 5$