Страница 80 номер 215, ГДЗ по алгебре за 10-11 класс Алимов - ответы и решение

1) \(0{,}3^{x^{3} - x^{2} + x - 1} = 1\)
\(0{,}3^{x^{3} - x^{2} + x - 1} = 0{,}3^{0},\)
\(x^{3} - x^{2} + x - 1 = 0,\)
\(x^{2}(x - 1) + (x - 1) = 0,\)
\((x - 1)(x^{2} + 1) = 0, x = 1,\) т.к. \(x^{2} + 1 \neq 0.\)

2) \(\left(2\frac{1}{3}\right)^{-x^{2} - 2x + 3} = 1\)
\(\left(2\dfrac{1}{3}\right)^{-x^{2} - 2x + 3} = \left(2\dfrac{1}{3}\right)^{0},\)
\(-x^{2} - 2x + 3 = 0,\)
\(x^{2} + 2x - 3 = 0,\)
\(x_{1{,}2} = \dfrac{-2 \pm \sqrt{4 + 12}}{2},\)
\(x_{1} = 1, x_{2} = -3;\)

3) \(5{,}1^{\frac{1}{2}(x - 3)} = 5{,}1\sqrt{5{,}1}\)
\(5{,}1^{\frac{1}{2}(x - 3)} = 5{,}1^{\frac{3}{2}},\)
\(\dfrac{1}{2}(x - 3) = \dfrac{3}{2},\)
\(x = 6;\)

4) \(100^{x^{2} - 1} = 10^{1 - 5x}\)
\(10^{2x^{2} - 2} = 10^{1 - 5x},\)
\(2x^{2} - 2 = 1 - 5x,\)
\(2x^{2} + 5x - 3 = 0,\)
\(x_{1{,}2} = \dfrac{-5 \pm \sqrt{25 + 24}}{4},\)
\(x_{1} = \dfrac{1}{2}, x_{2} = -3.\)