§ 4. Упражнение 315. «Математика. Алгебра. 8 класс. Базовый уровень.» АЛГЕБРА 8 ГДЗ Упражнение 315

    Упражнение 315

    Решите уравнение:
    \(\vphantom{\frac{0}{0}}{\largeа)}\ 80+y^2=81;\)
    \(\vphantom{\frac{0}{0}}{\largeб)}\ 19+с^2=10;\)
    \(\vphantom{\frac{0}{0}}{\largeв)}\ 20-b^2={-}5;\)
    \(\vphantom{\frac{0}{0}}{\largeг)}\ 3x^2=1{,}47;\)
    \({\largeд)}\ \frac{1}{4}a^2=10;\)
    \(\vphantom{\frac{0}{0}}{\largeе)}\ {-}5y^2=1{,}8.\)
    Источник заимствования: Математика. Алгебра. 8 класс. Базовый уровень. / – Просвещение, 2023. – 76 c. ISBN 978-5-09-102536-1
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    Решение:

    \(\vphantom{\frac{0}{0}}{\largeа)}\ 80+y^2=81\)
    \(\phantom{\largeа)}\ y^2=81-80\)
    \(\phantom{\largeа)}\ y^2=1\)
    \(\phantom{\largeа)\ }\begin{array}[t]{ll}y_1={-}\sqrt1&\largeи&y_2=\sqrt1\\[-1ex]\\y_1={-}1&\largeи&y_2=1\end{array}\)
    \(\vphantom{\frac{0}{0}}{\largeб)}\ 19+c^2=10\)
    \(\phantom{\largeб)}\ c^2=10-19\)
    \(\phantom{\largeб)}\ c^2={-}9\)
    \(\phantom{\largeб)\ }\)нет корней
    \(\vphantom{\frac{0}{0}}{\largeв)}\ 20-b^2={-}5\)
    \(\phantom{\largeв)}\ b^2=20+5\)
    \(\phantom{\largeв)}\ b^2=25\)
    \(\phantom{\largeв)\ }\begin{array}[t]{ll}b_1={-}\sqrt{25}&\largeи&b_2=\sqrt{25}\\[-1ex]\\b_1={-}5&\largeи&b_2=5\end{array}\)
    \(\vphantom{\frac{0}{0}}{\largeг)}\ 3x^2=1{,}47\)
    \(\phantom{\largeг)}\ x^2=1{,}47:3\)
    \(\phantom{\largeг)}\ x^2=0{,}49\)
    \(\phantom{\largeг)\ }\begin{array}[t]{ll}x_1={-}\sqrt{0{,}49}&\largeи&x_2=\sqrt{0{,}49}\\[-1ex]\\x_1={-}0{,}7&\largeи&x_2=0{,}7\end{array}\)
    \({\largeд)}\ \frac{1}{4}a^2=10\)
    \(\phantom{\largeд)}\ a^2=10:\frac{1}{4}\)
    \(\phantom{\largeд)}\ a^2=10\cdot4\)
    \(\phantom{\largeд)}\ a^2=40\)
    \(\phantom{\largeд)\ }\begin{array}[t]{ll}a_1={-}\sqrt{40}&\largeи&a_2=\sqrt{40}\end{array}\)
    \(\vphantom{\frac{0}{0}}{\largeе)}\ {-}5y^2=1{,}8\)
    \(\phantom{\largeе)}\ y^2=1{,}8:({-}5)\)
    \(\phantom{\largeе)}\ y^2={-}0{,}36\)
    \(\phantom{\largeе)\ }\)нет корней