(10+22+67+54+34+85+18+9+58+12):10=369:10=36,9
1) Уравнение
![x^{2} =a](https://tex.z-dn.net/?f=+x%5E%7B2%7D+%3Da)
имеет два корня при
![a>0](https://tex.z-dn.net/?f=a%3E0)
, один корень х=0 при
![a=0](https://tex.z-dn.net/?f=a%3D0)
, не имеет корней при
![a<0](https://tex.z-dn.net/?f=a%3C0)
.
а)
б)
в)
г )
д)
![2 x^{2} +6=0; x^{2} =-3;](https://tex.z-dn.net/?f=2+x%5E%7B2%7D+%2B6%3D0%3B+x%5E%7B2%7D+%3D-3%3B)
корней нет.
е)
![(x- \frac{1}{9}) ^{2}= \frac{4}{81}; x- \frac{1}{9}= \frac{2}{9};x=\frac{3}{9}; x- \frac{1}{9}=- \frac{2}{9};x=-\frac{1}{9};](https://tex.z-dn.net/?f=%28x-+%5Cfrac%7B1%7D%7B9%7D%29+%5E%7B2%7D%3D+%5Cfrac%7B4%7D%7B81%7D%3B+x-+%5Cfrac%7B1%7D%7B9%7D%3D+%5Cfrac%7B2%7D%7B9%7D%3Bx%3D%5Cfrac%7B3%7D%7B9%7D%3B+x-+%5Cfrac%7B1%7D%7B9%7D%3D-+%5Cfrac%7B2%7D%7B9%7D%3Bx%3D-%5Cfrac%7B1%7D%7B9%7D%3B+)
2) Выражение
![\sqrt{10-3x}](https://tex.z-dn.net/?f=+%5Csqrt%7B10-3x%7D+)
имеет смысл при
![x \leq 3 \frac{1}{3}](https://tex.z-dn.net/?f=x+%5Cleq+3+%5Cfrac%7B1%7D%7B3%7D+)
;
а)
![x=2;2\in(-\infty;3 \frac{1}{3} ]](https://tex.z-dn.net/?f=x%3D2%3B2%5Cin%28-%5Cinfty%3B3+%5Cfrac%7B1%7D%7B3%7D+%5D)
выражение имеет смысл.
б)
![x=0;0\in(-\infty;3 \frac{1}{3} ]](https://tex.z-dn.net/?f=x%3D0%3B0%5Cin%28-%5Cinfty%3B3+%5Cfrac%7B1%7D%7B3%7D+%5D)
выражение имеет смысл.
в)
![x=4;](https://tex.z-dn.net/?f=x%3D4%3B)
4 не принадлежит
![(-\infty;3 \frac{1}{3} ]](https://tex.z-dn.net/?f=%28-%5Cinfty%3B3+%5Cfrac%7B1%7D%7B3%7D+%5D)
выражение не имеет смысла.
г)
![x=-1;-1\in(-\infty;3 \frac{1}{3} ]](https://tex.z-dn.net/?f=x%3D-1%3B-1%5Cin%28-%5Cinfty%3B3+%5Cfrac%7B1%7D%7B3%7D+%5D)
выражение имеет смысл.
3) а)
![(- \sqrt{11} )^2=11](https://tex.z-dn.net/?f=%28-+%5Csqrt%7B11%7D+%29%5E2%3D11)
б)
![-3 \sqrt{6}* \sqrt{6}=-18](https://tex.z-dn.net/?f=-3+%5Csqrt%7B6%7D%2A++%5Csqrt%7B6%7D%3D-18+)
в)
![(- 2\sqrt{10} )^2=40](https://tex.z-dn.net/?f=%28-+2%5Csqrt%7B10%7D+%29%5E2%3D40)
г)
![( \frac{ \sqrt{3} }{4} )^2= \frac{3}{16}](https://tex.z-dn.net/?f=%28+%5Cfrac%7B+%5Csqrt%7B3%7D+%7D%7B4%7D+%29%5E2%3D+%5Cfrac%7B3%7D%7B16%7D+)
D=4-4*5*а=4-20а<0 тогда нет корней
4-20a<0
-20a<-4
a>-4/-20
a>1/5
a>0.2
при а (0,2;+∞)
![\frac{ (a+b)^{2}- (ab+1)^{2} }{( a^{2} -1)( b^{2} -1)} = \frac{( a^{2}+2ab+ b^{2})-( a^{2} b^{2} +2ab+1)}{( a^{2}-1)( b^{2} -1) } = \frac{ a^{2}+ b^{2} - a^{2}b^{2}-1 }{( a^{2} -1)(b^{2} -1)} =](https://tex.z-dn.net/?f=+%5Cfrac%7B+%28a%2Bb%29%5E%7B2%7D-+%28ab%2B1%29%5E%7B2%7D++%7D%7B%28+a%5E%7B2%7D+-1%29%28+b%5E%7B2%7D+-1%29%7D+%3D+%5Cfrac%7B%28+a%5E%7B2%7D%2B2ab%2B+b%5E%7B2%7D%29-%28+a%5E%7B2%7D++b%5E%7B2%7D+%2B2ab%2B1%29%7D%7B%28+a%5E%7B2%7D-1%29%28+b%5E%7B2%7D+-1%29+%7D+%3D++%5Cfrac%7B+a%5E%7B2%7D%2B+b%5E%7B2%7D+-+a%5E%7B2%7Db%5E%7B2%7D-1+%7D%7B%28+a%5E%7B2%7D+-1%29%28b%5E%7B2%7D+-1%29%7D+%3D+)
![\frac{( a^{2} -1)-( a^{2}b^{2} - b^{2} )}{( a^{2} -1)(b^{2} -1)} = \frac{( a^{2} -1)- b^{2} ( a^{2} -1)}{( a^{2} -1)( b^{2} -1)} = \frac{( a^{2} -1)(1- b^{2} )}{( a^{2} -1)( b^{2} -1)} = \frac{1- b^{2} }{ b^{2} -1} = -\frac{b^{2} -1}{b^{2} -1} =-1](https://tex.z-dn.net/?f=+%5Cfrac%7B%28+a%5E%7B2%7D+-1%29-%28+a%5E%7B2%7Db%5E%7B2%7D+-+b%5E%7B2%7D+%29%7D%7B%28+a%5E%7B2%7D+-1%29%28b%5E%7B2%7D+-1%29%7D+%3D+%5Cfrac%7B%28+a%5E%7B2%7D+-1%29-+b%5E%7B2%7D+%28+a%5E%7B2%7D+-1%29%7D%7B%28+a%5E%7B2%7D+-1%29%28+b%5E%7B2%7D+-1%29%7D+%3D+%5Cfrac%7B%28+a%5E%7B2%7D+-1%29%281-+b%5E%7B2%7D+%29%7D%7B%28+a%5E%7B2%7D+-1%29%28+b%5E%7B2%7D+-1%29%7D+%3D+%5Cfrac%7B1-+b%5E%7B2%7D+%7D%7B+b%5E%7B2%7D+-1%7D+%3D+-%5Cfrac%7Bb%5E%7B2%7D+-1%7D%7Bb%5E%7B2%7D+-1%7D+%3D-1)
Ответ: - 1 при любых значениях переменных a и b,