Question

x - y = 7 ; xy = -2 , Hallar x³ - y³

Answer 1

Respuesta:

301

Explicación paso a paso:

$( {x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} \\ ( {7})^{2} = {x}^{2} - 2( - 2) + {y}^{2} \\ 49 = {x}^{2} + 4 + {y}^{2} \\ 45 = {x}^{2} + {y}^{2} \\ \ {x}^{3} - {y}^{3} = (x - y)( {x}^{2} +xy + {y}^{2} ) \\ {x}^{3} - {y}^{3} = (7)(45 + ( - 2)) \\ {x}^{3} - {y}^{3} = (7)(43) \\ {x}^{3} - {y}^{3} = 301$