Question

помогите срочно!!!!
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Answer 1

Ответ:

по теореме Виета

$x_{1} +x_{2} = -10\\x_{1} x_{2} = -4$

а) $\frac{1}{x_{1}^2} + \frac{1}{x_{2} ^2} = \frac{x_{2}^2 +x_{1}^2}{(x_{1} x_{2})^2} = \frac{(x_{1} +x_{2})^2 - 2x_{1} x_{2}}{(x_{1} x_{2})^2} = \frac{(-10)^2-2*(-4)}{(-4)^2} = \frac{100+8}{16} = \frac{108}{16} = 6.75$

б)

$(x_{1}- x_{2})^2 = x_{1}^2- 2x_{1} x_{2}+x_{2} ^2 = (x_{1} +x_{2})^2 - 4x_{1} x_{2} = (-10)^2-4*(-4) = 100+16 = 116$

в)

$x_{1} ^3 +x_{2}^3 = (x_{1} +x_{2})(x_{1}^2 - x_{1} x_{2}+ x_{2}^2) =\\= (x_{1} +x_{2})( (x_{1} +x_{2})^2 - 3x_{1} x_{2} ) =(-10)((-10)^2-3*(-4)) = (-10)(100+12) = -1120$

г)

$x_{1}^2x_{2}+x_{1} x_{2}^2 = x_{1}x_{2}( x_{1}+x_{2}) = -4*(-10) = 40$