Найдите корни уравнения:
\({\largeа)}\ \sqrt{12+x}-7=3;\)
\({\largeб)}\ \sqrt{5x-1}-4=6;\)
\({\largeв)}\ 16-\sqrt{x-2}=7;\)
\({\largeг)}\ 12-\sqrt{3-6x}={-}2.\)
Упражнение 308
Источник заимствования: Математика. Алгебра. 8 класс. Базовый уровень. / Ю.Н. Макарычев, Н.Г. Миндюк, К.И. Нешков, С.Б. Суворова – Просвещение, 2023. – 74 c. ISBN 978-5-09-102536-1
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Решение:
\({\largeа)}\ \sqrt{12+x}-7=3\)
\(\phantom{\largeа)}\ \sqrt{12+x}=3+7\)
\(\phantom{\largeа)}\ \sqrt{12+x}=10\)
\(\phantom{\largeа)}\ 12+x=10^2\)
\(\phantom{\largeа)}\ 12+x=100\)
\(\phantom{\largeа)}\ x=100-12\)
\(\phantom{\largeа)}\ x=88\)
\(\phantom{\largeа)}\ \sqrt{12+x}=3+7\)
\(\phantom{\largeа)}\ \sqrt{12+x}=10\)
\(\phantom{\largeа)}\ 12+x=10^2\)
\(\phantom{\largeа)}\ 12+x=100\)
\(\phantom{\largeа)}\ x=100-12\)
\(\phantom{\largeа)}\ x=88\)
\({\largeб)}\ \sqrt{5x-1}-4=6\)
\(\phantom{\largeб)}\ \sqrt{5x-1}=6+4\)
\(\phantom{\largeб)}\ \sqrt{5x-1}=10\)
\(\phantom{\largeб)}\ 5x-1=10^2\)
\(\phantom{\largeб)}\ 5x-1=100\)
\(\phantom{\largeб)}\ 5x=100+1\)
\(\phantom{\largeб)}\ 5x=101\)
\(\phantom{\largeб)}\ x=\frac{101}{5}\)
\(\phantom{\largeб)}\ x=20\frac{1}{5}\)
\(\phantom{\largeб)}\ \sqrt{5x-1}=6+4\)
\(\phantom{\largeб)}\ \sqrt{5x-1}=10\)
\(\phantom{\largeб)}\ 5x-1=10^2\)
\(\phantom{\largeб)}\ 5x-1=100\)
\(\phantom{\largeб)}\ 5x=100+1\)
\(\phantom{\largeб)}\ 5x=101\)
\(\phantom{\largeб)}\ x=\frac{101}{5}\)
\(\phantom{\largeб)}\ x=20\frac{1}{5}\)
\({\largeв)}\ 16-\sqrt{x-2}=7\)
\(\phantom{\largeв)}\ \sqrt{x-2}=16-7\)
\(\phantom{\largeв)}\ \sqrt{x-2}=9\)
\(\phantom{\largeв)}\ x-2=9^2\)
\(\phantom{\largeв)}\ x-2=81\)
\(\phantom{\largeв)}\ x=81+2\)
\(\phantom{\largeв)}\ x=83\)
\(\phantom{\largeв)}\ \sqrt{x-2}=16-7\)
\(\phantom{\largeв)}\ \sqrt{x-2}=9\)
\(\phantom{\largeв)}\ x-2=9^2\)
\(\phantom{\largeв)}\ x-2=81\)
\(\phantom{\largeв)}\ x=81+2\)
\(\phantom{\largeв)}\ x=83\)
\({\largeг)}\ 12-\sqrt{3-6x}={-}2\)
\(\phantom{\largeг)}\ \sqrt{3-6x}=12+2\)
\(\phantom{\largeг)}\ \sqrt{3-6x}=14\)
\(\phantom{\largeг)}\ 3-6x=14^2\)
\(\phantom{\largeг)}\ 3-6x=196\)
\(\phantom{\largeг)}\ 6x=3-196\)
\(\phantom{\largeг)}\ 6x={-}193\)
\(\phantom{\largeг)}\ x={-}\frac{193}{6}\)
\(\phantom{\largeг)}\ x={-}32\frac{1}{6}\)
\(\phantom{\largeг)}\ \sqrt{3-6x}=12+2\)
\(\phantom{\largeг)}\ \sqrt{3-6x}=14\)
\(\phantom{\largeг)}\ 3-6x=14^2\)
\(\phantom{\largeг)}\ 3-6x=196\)
\(\phantom{\largeг)}\ 6x=3-196\)
\(\phantom{\largeг)}\ 6x={-}193\)
\(\phantom{\largeг)}\ x={-}\frac{193}{6}\)
\(\phantom{\largeг)}\ x={-}32\frac{1}{6}\)