Наверно : вычислить значения выражения: 1/x₁² +1/x₂² .
D =5² -4*1(-17) = 93>0 имеет корней
1/x₁² +1/x₂² =(x₂² +x₁²) /x₁²*x₂² =((x₁+x₂)² -2x₁*x₂)/(x₁*x₂)² =(5² -2*(-17))/(-17)² =59/289.
√245=√(5*49)=7√5
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I. При любых, т.к. корень 3й степени может быть как из положительных, так из отрицательных чисел
II .Только, если подкоренное выражение больше или равно 0. Соответственно
<span>
ОДЗ
2х-4</span>≠0
х≠2
<span>2-3x
------ >0
2x-4
</span>2-3х>0 или 2-3х<0
и и
2х-4>0 <span>2х-4<0
3х<2 </span>3х>2 <span>
и и
2х>4 </span>2х<4<span>
x<2/3 x>2/3
и и
х>2 x<2
</span>
х∈[2/3;2)
2)
![( \sqrt{3+ \sqrt{5} } - \sqrt{3- \sqrt{5} })^2= \\ (\sqrt{3+ \sqrt{5} })^2-2*\sqrt{3+ \sqrt{5} }*\sqrt{3- \sqrt{5} }+(\sqrt{3- \sqrt{5} })^2= \\ 3+ \sqrt{5}-2*\sqrt{(3+ \sqrt{5})*(\sqrt{3- \sqrt{5} })}+3- \sqrt{5}= \\ 6+2*\sqrt{3^2- \sqrt{5}^2}=6+2* \sqrt{9-5}= 6+2* \sqrt{4}= \\ 6+2*2=6+4=10](https://tex.z-dn.net/?f=%28+%5Csqrt%7B3%2B+%5Csqrt%7B5%7D+%7D+-+%5Csqrt%7B3-+%5Csqrt%7B5%7D+%7D%29%5E2%3D+%5C%5C+%28%5Csqrt%7B3%2B+%5Csqrt%7B5%7D+%7D%29%5E2-2%2A%5Csqrt%7B3%2B+%5Csqrt%7B5%7D+%7D%2A%5Csqrt%7B3-+%5Csqrt%7B5%7D+%7D%2B%28%5Csqrt%7B3-+%5Csqrt%7B5%7D+%7D%29%5E2%3D+%5C%5C+3%2B+%5Csqrt%7B5%7D-2%2A%5Csqrt%7B%283%2B+%5Csqrt%7B5%7D%29%2A%28%5Csqrt%7B3-+%5Csqrt%7B5%7D+%7D%29%7D%2B3-+%5Csqrt%7B5%7D%3D+%5C%5C+6%2B2%2A%5Csqrt%7B3%5E2-+%5Csqrt%7B5%7D%5E2%7D%3D6%2B2%2A+%5Csqrt%7B9-5%7D%3D+6%2B2%2A+%5Csqrt%7B4%7D%3D+%5C%5C++6%2B2%2A2%3D6%2B4%3D10)
3)
![\frac{ \sqrt{3}+ \sqrt{2} }{\sqrt{3}- \sqrt{2}} - \frac{ \sqrt{3}- \sqrt{2} }{\sqrt{3}+ \sqrt{2}}= \\ \frac{ (\sqrt{3}+ \sqrt{2})^2 }{(\sqrt{3}- \sqrt{2})(\sqrt{3}+ \sqrt{2})} - \frac{ (\sqrt{3}- \sqrt{2})^2 }{(\sqrt{3}- \sqrt{2})(\sqrt{3}+ \sqrt{2})}= \\ \frac{ (\sqrt{3}+ \sqrt{2})^2- (\sqrt{3}- \sqrt{2})^2 }{(\sqrt{3}- \sqrt{2})(\sqrt{3}+ \sqrt{2})}= \\ \frac{ (\sqrt{3}+ \sqrt{2}-(\sqrt{3}- \sqrt{2}))(\sqrt{3}+ \sqrt{2}+(\sqrt{3}- \sqrt{2})) }{\sqrt{3}^2- \sqrt{2}^2}= \\](https://tex.z-dn.net/?f=+%5Cfrac%7B+%5Csqrt%7B3%7D%2B+%5Csqrt%7B2%7D+%7D%7B%5Csqrt%7B3%7D-+%5Csqrt%7B2%7D%7D+-+%5Cfrac%7B+%5Csqrt%7B3%7D-+%5Csqrt%7B2%7D+%7D%7B%5Csqrt%7B3%7D%2B+%5Csqrt%7B2%7D%7D%3D+%5C%5C++%5Cfrac%7B+%28%5Csqrt%7B3%7D%2B+%5Csqrt%7B2%7D%29%5E2+%7D%7B%28%5Csqrt%7B3%7D-+%5Csqrt%7B2%7D%29%28%5Csqrt%7B3%7D%2B+%5Csqrt%7B2%7D%29%7D+-+%5Cfrac%7B+%28%5Csqrt%7B3%7D-+%5Csqrt%7B2%7D%29%5E2+%7D%7B%28%5Csqrt%7B3%7D-+%5Csqrt%7B2%7D%29%28%5Csqrt%7B3%7D%2B+%5Csqrt%7B2%7D%29%7D%3D+%5C%5C+%5Cfrac%7B+%28%5Csqrt%7B3%7D%2B+%5Csqrt%7B2%7D%29%5E2-+%28%5Csqrt%7B3%7D-+%5Csqrt%7B2%7D%29%5E2+%7D%7B%28%5Csqrt%7B3%7D-+%5Csqrt%7B2%7D%29%28%5Csqrt%7B3%7D%2B+%5Csqrt%7B2%7D%29%7D%3D+%5C%5C++%5Cfrac%7B+%28%5Csqrt%7B3%7D%2B+%5Csqrt%7B2%7D-%28%5Csqrt%7B3%7D-+%5Csqrt%7B2%7D%29%29%28%5Csqrt%7B3%7D%2B+%5Csqrt%7B2%7D%2B%28%5Csqrt%7B3%7D-+%5Csqrt%7B2%7D%29%29+%7D%7B%5Csqrt%7B3%7D%5E2-+%5Csqrt%7B2%7D%5E2%7D%3D+%5C%5C)
![\frac{ (\sqrt{3}+ \sqrt{2}-\sqrt{3}+ \sqrt{2})(\sqrt{3}+ \sqrt{2}+\sqrt{3}- \sqrt{2}) }{\sqrt{3}^2- \sqrt{2}^2}= \\ \frac{ (2 \sqrt{2})(2\sqrt{3}) }{\sqrt{3}^2- \sqrt{2}^2}= \frac{4 \sqrt{6} }{3-2}= \frac{4 \sqrt{6} }{1}= 4 \sqrt{6}](https://tex.z-dn.net/?f=%5Cfrac%7B+%28%5Csqrt%7B3%7D%2B+%5Csqrt%7B2%7D-%5Csqrt%7B3%7D%2B+%5Csqrt%7B2%7D%29%28%5Csqrt%7B3%7D%2B+%5Csqrt%7B2%7D%2B%5Csqrt%7B3%7D-+%5Csqrt%7B2%7D%29+%7D%7B%5Csqrt%7B3%7D%5E2-+%5Csqrt%7B2%7D%5E2%7D%3D+%5C%5C+%5Cfrac%7B+%282+%5Csqrt%7B2%7D%29%282%5Csqrt%7B3%7D%29+%7D%7B%5Csqrt%7B3%7D%5E2-+%5Csqrt%7B2%7D%5E2%7D%3D+%5Cfrac%7B4+%5Csqrt%7B6%7D+%7D%7B3-2%7D%3D+%5Cfrac%7B4+%5Csqrt%7B6%7D+%7D%7B1%7D%3D+4+%5Csqrt%7B6%7D)