§ 10. Иррациональные уравнения
Задачи 3.411 – 3.440 с ответами
Решение уравнение:
3.411 \(\displaystyle\sqrt{x+1+\sqrt{2}}=\sqrt[4]{2}\)
3.412 \(\displaystyle\sqrt{\sqrt{3}-x}=\sqrt[4]{3}\)
3.413 \(\displaystyle\sqrt{3+2\sqrt{2}}=\sqrt{2\sqrt{2}}\)
3.414 \(\displaystyle\sqrt{x-2\sqrt{3}-1}=\sqrt{3}-1\)
3.415 \(\displaystyle\sqrt{3x+4\sqrt{5}}=\sqrt{5}+2\)
3.416 \(\displaystyle\sqrt{6\sqrt{3}-x}=\sqrt{3}+3\)
3.417 \(\displaystyle\sqrt{x+7+2\sqrt{6}}=\sqrt{3}+\sqrt{2}\)
3.418 \(\displaystyle\sqrt{2x-2\sqrt{10}+4}=\sqrt{5}-\sqrt{2}\)
3.419 \(\displaystyle\sqrt{2\sqrt{14}-x}=\sqrt{7}+\sqrt{2}\)
3.420 \(\displaystyle\sqrt{2\cdot\sqrt[4]{2}+2x+\sqrt{2}}=\sqrt[4]{2}+1\)
Решите уравнение:
3.421 \(\displaystyle\sqrt{\frac{9-5x}{3-8x}}=\frac{1}{\sqrt{2}}\)
3.422 \(\displaystyle\sqrt{\frac{4-x}{x+2}}=\frac{1}{\sqrt{3}}\)
3.423 \(\displaystyle\sqrt{\frac{x+1}{x-1}}=3\)
3.424 \(\displaystyle\sqrt{\frac{19-2x}{2-x}}=\frac{3}{2}\)
3.425 \(\displaystyle\sqrt{\frac{2+x}{2x+1}}=\sqrt{3}\)
3.426 \(\displaystyle\sqrt{\frac{x+3}{x+4}}=\frac{1}{\sqrt{5}}\)
3.427 \(\displaystyle\sqrt{\frac{x-4}{2-3x}}=1\)
3.428 \(\displaystyle\sqrt{\frac{x}{x+1}}-\frac{1}{\sqrt{6}}=0\)
3.429 \(\displaystyle\sqrt{\frac{6-2x}{5+x}}=\sqrt{2}\)
3.430 \(\displaystyle\sqrt{\frac{2x-7}{x+6}}=\sqrt{\frac{5}{2}}\)
Решите уравнение:
3.431 \(\displaystyle\sqrt{\frac{1}{1-x}+\frac{1}{x}}=\frac{2}{\sqrt{1-x}}\)
3.432 \(\displaystyle\sqrt{\frac{1}{x-1}-\frac{3}{2x}}=\frac{1}{\sqrt{2x}}\)
3.433 \(\displaystyle\sqrt{2-\frac{x}{x+1}}=\frac{4}{\sqrt{x+1}}\)
3.434 \(\displaystyle\sqrt{\frac{2}{x+3}-\frac{1}{x+1}}=\sqrt{\frac{3}{x+3}}\)
3.435 \(\displaystyle\sqrt{\frac{x+1}{x-3}-\frac{x}{x+2}}=\frac{1}{\sqrt{x+2}}\)
3.436 \(\displaystyle\sqrt{\frac{x}{1-x}+\frac{1+x}{x}}=\frac{2}{\sqrt{x}}\)
3.437 \(\displaystyle\sqrt{\frac{1}{x-1}+\frac{1}{2}}=\frac{3}{\sqrt{x-1}}\)
3.438 \(\displaystyle\sqrt{\frac{1}{2x}-\frac{1}{2x+1}}=\frac{1}{\sqrt{3x}}\)
3.439 \(\displaystyle\sqrt{\frac{2x}{x^2-1}}=\frac{2}{\sqrt{x+1}}\)
3.440 \(\displaystyle\sqrt{\frac{31-x}{9-x^2}}=\frac{3}{\sqrt{3-x}}\)
Ответы
3.411 -1
3.412 0
3.413 0
3.414 5
3.415 3
3.416 -12
3.417 -2
3.418 1,5
3.419 -9
3.420 0,5
3.421 7,5
3.422 2,5
3.423 1,25
3.424 32
3.425 -0,2
3.426 -2,75
3.427 1,5
3.428 0,2
3.429 -1
3.430 -44
3.431 0,25
3.432 4
3.433 14
3.434 -2
3.435 -1
3.436 0,75
3.437 17
3.438 0,25
3.439 2
3.440 0,4