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1)![sqrt[3]{x-2}+sqrt{x-1}=5\
x-1=t\
sqrt[3]{t-1}+sqrt{t}=5\
sqrt[3]{t-1}=5-sqrt{t}\
t-1 = (5-sqrt{t})^3\
t-1=15t-tsqrt{t}-75sqrt{t}+125\
14t-tsqrt{t}-75sqrt{t}+126=0\](https://tex.z-dn.net/?f=sqrt%5B3%5D%7Bx-2%7D%2Bsqrt%7Bx-1%7D%3D5%5C%0Ax-1%3Dt%5C%0Asqrt%5B3%5D%7Bt-1%7D%2Bsqrt%7Bt%7D%3D5%5C%0A+sqrt%5B3%5D%7Bt-1%7D%3D5-sqrt%7Bt%7D%5C%0At-1+%3D+%285-sqrt%7Bt%7D%29%5E3%5C%0At-1%3D15t-tsqrt%7Bt%7D-75sqrt%7Bt%7D%2B125%5C%0A14t-tsqrt%7Bt%7D-75sqrt%7Bt%7D%2B126%3D0%5C%0A "sqrt[3]{x-2}+sqrt{x-1}=5\
x-1=t\
sqrt[3]{t-1}+sqrt{t}=5\
sqrt[3]{t-1}=5-sqrt{t}\
t-1 = (5-sqrt{t})^3\
t-1=15t-tsqrt{t}-75sqrt{t}+125\
14t-tsqrt{t}-75sqrt{t}+126=0\")
теперь для упрощения сделаем еще замену
![t^{frac{1}{2}}=a\
t^{frac{1}{2}}=a^2\
14a^2-a^3-75a+126=0\
a=3\
t=9\
x=10](https://tex.z-dn.net/?f=t%5E%7Bfrac%7B1%7D%7B2%7D%7D%3Da%5C%0At%5E%7Bfrac%7B1%7D%7B2%7D%7D%3Da%5E2%5C%0A14a%5E2-a%5E3-75a%2B126%3D0%5C%0Aa%3D3%5C%0At%3D9%5C%0Ax%3D10 "t^{frac{1}{2}}=a\
t^{frac{1}{2}}=a^2\
14a^2-a^3-75a+126=0\
a=3\
t=9\
x=10")
Ответ х=10
2) Не видно что в последней строке написано
3)![left { {{sqrt{x}-sqrt{y}=0.5sqrt{xy}} atop {x+y=5}} right. \
\
zamena x=a^2\
y=b^2\\
a-b=0.5ab\
a^2+b^2=5\
\
2a-2b-ab=0\
a=sqrt{5-b^2}\
2sqrt{5-b^2}-2b-sqrt{5-b^2}*b=0\
b=1\
a=2\
\
x=4\
y=1](https://tex.z-dn.net/?f=+left+%7B+%7B%7Bsqrt%7Bx%7D-sqrt%7By%7D%3D0.5sqrt%7Bxy%7D%7D+atop+%7Bx%2By%3D5%7D%7D+right.+%5C%0A%5C%0Azamena+x%3Da%5E2%5C%0A+++++++++++++++y%3Db%5E2%5C%5C%0Aa-b%3D0.5ab%5C%0Aa%5E2%2Bb%5E2%3D5%5C%0A%5C%0A2a-2b-ab%3D0%5C%0Aa%3Dsqrt%7B5-b%5E2%7D%5C%0A2sqrt%7B5-b%5E2%7D-2b-sqrt%7B5-b%5E2%7D%2Ab%3D0%5C%0Ab%3D1%5C%0Aa%3D2%5C%0A%5C%0Ax%3D4%5C%0Ay%3D1++++%0A "left { {{sqrt{x}-sqrt{y}=0.5sqrt{xy}} atop {x+y=5}} right. \
\
zamena x=a^2\
y=b^2\\
a-b=0.5ab\
a^2+b^2=5\
\
2a-2b-ab=0\
a=sqrt{5-b^2}\
2sqrt{5-b^2}-2b-sqrt{5-b^2}*b=0\
b=1\
a=2\
\
x=4\
y=1")
![4)\
2y+3x+2=16\
4y-2x-3=(3x-3)^2\
\
2y+3x=14\
4y-2x-3=9x^2-18x+9\
\
2y+3x=14\
9x^2-16x-4y+12=0\
\
y=frac{14-3x}{2}\
9x^2-16x-4frac{14-3x}{2}+12=0\
x=2\
y=4\](https://tex.z-dn.net/?f=4%29%5C%0A+2y%2B3x%2B2%3D16%5C%0A+4y-2x-3%3D%283x-3%29%5E2%5C%0A%5C%0A2y%2B3x%3D14%5C%0A4y-2x-3%3D9x%5E2-18x%2B9%5C%0A%5C%0A2y%2B3x%3D14%5C%0A+9x%5E2-16x-4y%2B12%3D0%5C%0A%5C%0A+y%3Dfrac%7B14-3x%7D%7B2%7D%5C%0A9x%5E2-16x-4frac%7B14-3x%7D%7B2%7D%2B12%3D0%5C%0Ax%3D2%5C%0Ay%3D4%5C%0A "4)\
2y+3x+2=16\
4y-2x-3=(3x-3)^2\
\
2y+3x=14\
4y-2x-3=9x^2-18x+9\
\
2y+3x=14\
9x^2-16x-4y+12=0\
\
y=frac{14-3x}{2}\
9x^2-16x-4frac{14-3x}{2}+12=0\
x=2\
y=4\")
![5)\
sqrt{frac{x+1}{y+2}}- sqrt{frac{y+2}{x+1}}=1.5\
x-2y=13\
\
zamena frac{x+1}{y+2}=t\
sqrt{t}-sqrt{frac{1}{t}}=1.5\
x=13+2y\
frac{13+2y+1}{y+2}=t\
frac{y+2}{13+2y+1}=frac{1}{t}\
sqrt{t}-sqrt{frac{1}{t}}=1.5\
x=19\
y=3](https://tex.z-dn.net/?f=5%29%5C%0A++sqrt%7Bfrac%7Bx%2B1%7D%7By%2B2%7D%7D-+sqrt%7Bfrac%7By%2B2%7D%7Bx%2B1%7D%7D%3D1.5%5C%0A++x-2y%3D13%5C%0A%5C%0Azamena++frac%7Bx%2B1%7D%7By%2B2%7D%3Dt%5C%0A++sqrt%7Bt%7D-sqrt%7Bfrac%7B1%7D%7Bt%7D%7D%3D1.5%5C%0A+++x%3D13%2B2y%5C%0A+frac%7B13%2B2y%2B1%7D%7By%2B2%7D%3Dt%5C%0A+frac%7By%2B2%7D%7B13%2B2y%2B1%7D%3Dfrac%7B1%7D%7Bt%7D%5C%0Asqrt%7Bt%7D-sqrt%7Bfrac%7B1%7D%7Bt%7D%7D%3D1.5%5C%0Ax%3D19%5C%0Ay%3D3 "5)\
sqrt{frac{x+1}{y+2}}- sqrt{frac{y+2}{x+1}}=1.5\
x-2y=13\
\
zamena frac{x+1}{y+2}=t\
sqrt{t}-sqrt{frac{1}{t}}=1.5\
x=13+2y\
frac{13+2y+1}{y+2}=t\
frac{y+2}{13+2y+1}=frac{1}{t}\
sqrt{t}-sqrt{frac{1}{t}}=1.5\
x=19\
y=3")
теперь для упрощения сделаем еще замену
Ответ х=10
2) Не видно что в последней строке написано
3)
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