Question

Решить системы уравнений! С решением и пояснением. Буду очень благодарна!

Answer 1

1)
$left { {{-1- sqrt{17} textless x textless sqrt{17}, x neqsqrt{17}-1 } atop {7sqrt{17}+(sqrt{17}-7)x-x^2 geq sqrt{17}-x}} right. \ \ left { {{-1- sqrt{17} textless x textless sqrt{17}, x neqsqrt{17}-1 } atop {x^2+(6-sqrt{17})x-6sqrt{17} leq 0}} right.$
$x^2+(6-sqrt{17})x-6sqrt{17} = 0$
По теореме Виета:
$left[begin{array}{ccc}x_1=-6\x_2= sqrt{17} end{array}$
$left { {{-1- sqrt{17} textless x textless sqrt{17}, x neqsqrt{17}-1 } atop {-6 leq x leq sqrt{17}}} right$
x ∈ (-1 - √17; √17 - 1)∪(√17 - 1; √17)
2)
$left { {{-7 textless x textless -1-sqrt{17}} atop {7sqrt{17}+(sqrt{17}-7)x-x^2 leq sqrt{17}-x}} right. \ \ left { {{-7 textless x textless -1-sqrt{17}} atop {x^2+(6-sqrt{17})x-6sqrt{17} geq 0}} right$
$x^2+(6-sqrt{17})x-6sqrt{17} = 0$
По теореме Виета:
$left[begin{array}{ccc}x_1=-6\x_2= sqrt{17} end{array}$
$left { {{-7 textless x textless -1-sqrt{17}} atop {x leq -6,x geq sqrt{17} right$
x ∈ (-7; -6]