Answer:
![\sqrt{-12} = 2\sqrt{3} i\\\sqrt{-9}= 3i\\3i * 2\sqrt{3}i = -6\sqrt{3](https://tex.z-dn.net/?f=%5Csqrt%7B-12%7D%20%3D%202%5Csqrt%7B3%7D%20i%5C%5C%5Csqrt%7B-9%7D%3D%203i%5C%5C3i%20%2A%202%5Csqrt%7B3%7Di%20%3D%20-6%5Csqrt%7B3)
Step-by-step explanation:
Answer:
and ![y=-1,\frac{1}{2}](https://tex.z-dn.net/?f=y%3D-1%2C%5Cfrac%7B1%7D%7B2%7D)
The ordered pair solutions are
,
,
, and
.
Step-by-step explanation:
I'm assuming the system is
:
![x^2+y^2=2](https://tex.z-dn.net/?f=x%5E2%2By%5E2%3D2)
![x^2+(2x^2-3)^2=2](https://tex.z-dn.net/?f=x%5E2%2B%282x%5E2-3%29%5E2%3D2)
![x^2+(4x^4-12x^2+9)=2](https://tex.z-dn.net/?f=x%5E2%2B%284x%5E4-12x%5E2%2B9%29%3D2)
![x^2+4x^4-12x^2+9=2](https://tex.z-dn.net/?f=x%5E2%2B4x%5E4-12x%5E2%2B9%3D2)
![4x^4-11x^2+9=2](https://tex.z-dn.net/?f=4x%5E4-11x%5E2%2B9%3D2)
![4x^4-11x^2+7=0](https://tex.z-dn.net/?f=4x%5E4-11x%5E2%2B7%3D0)
![x^4-11x^2+28=0](https://tex.z-dn.net/?f=x%5E4-11x%5E2%2B28%3D0)
![(x^2-7)(x^2-4)=0](https://tex.z-dn.net/?f=%28x%5E2-7%29%28x%5E2-4%29%3D0)
![(4x^2-7)(x^2-1)=0](https://tex.z-dn.net/?f=%284x%5E2-7%29%28x%5E2-1%29%3D0)
![4x^2-7=0](https://tex.z-dn.net/?f=4x%5E2-7%3D0)
![4x^2=7](https://tex.z-dn.net/?f=4x%5E2%3D7)
![x^2=\frac{7}{4}](https://tex.z-dn.net/?f=x%5E2%3D%5Cfrac%7B7%7D%7B4%7D)
![x=\pm\sqrt{\frac{7}{4}}](https://tex.z-dn.net/?f=x%3D%5Cpm%5Csqrt%7B%5Cfrac%7B7%7D%7B4%7D%7D)
![x^2-1=0](https://tex.z-dn.net/?f=x%5E2-1%3D0)
![x^2=1](https://tex.z-dn.net/?f=x%5E2%3D1)
![x=\pm1](https://tex.z-dn.net/?f=x%3D%5Cpm1)
![y=2x^2-3](https://tex.z-dn.net/?f=y%3D2x%5E2-3)
![y=2(\pm\sqrt{\frac{7}{4}})^2-3](https://tex.z-dn.net/?f=y%3D2%28%5Cpm%5Csqrt%7B%5Cfrac%7B7%7D%7B4%7D%7D%29%5E2-3)
![y=2({\frac{7}{4}})-3](https://tex.z-dn.net/?f=y%3D2%28%7B%5Cfrac%7B7%7D%7B4%7D%7D%29-3)
![y=\frac{7}{2}-3](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B7%7D%7B2%7D-3)
![y=\frac{1}{2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B2%7D)
![y=2x^2-3](https://tex.z-dn.net/?f=y%3D2x%5E2-3)
![y=2(\pm1)^2-3](https://tex.z-dn.net/?f=y%3D2%28%5Cpm1%29%5E2-3)
![y=2(1)-3](https://tex.z-dn.net/?f=y%3D2%281%29-3)
![y=2-3](https://tex.z-dn.net/?f=y%3D2-3)
![y=-1](https://tex.z-dn.net/?f=y%3D-1)
Therefore,
and ![y=-1,\frac{1}{2}](https://tex.z-dn.net/?f=y%3D-1%2C%5Cfrac%7B1%7D%7B2%7D)
The ordered pair solutions are
,
,
, and
.
Answer:
The center of circle is
Step-by-step explanation:
We need to find the center of the circle of the equation ![x^{2}+y^{2}=4](https://tex.z-dn.net/?f=x%5E%7B2%7D%2By%5E%7B2%7D%3D4)
Since, the general equation of circle is ![(x-h)^{2}+(y-k)^{2} = r^{2}](https://tex.z-dn.net/?f=%28x-h%29%5E%7B2%7D%2B%28y-k%29%5E%7B2%7D%20%3D%20r%5E%7B2%7D)
Where (h,k) is center of circle and r is radius.
Re-write the circle equation is
as,
![x^{2}+y^{2}=2^{2}](https://tex.z-dn.net/?f=x%5E%7B2%7D%2By%5E%7B2%7D%3D2%5E%7B2%7D)
Compare
with ![(x-h)^{2}+(y-k)^{2} = r^{2}](https://tex.z-dn.net/?f=%28x-h%29%5E%7B2%7D%2B%28y-k%29%5E%7B2%7D%20%3D%20r%5E%7B2%7D)
so, ![(x-0)^{2}+(y-0)^{2} = 2^{2}](https://tex.z-dn.net/?f=%28x-0%29%5E%7B2%7D%2B%28y-0%29%5E%7B2%7D%20%3D%202%5E%7B2%7D)
Hence, the center of circle is ![(0,0)](https://tex.z-dn.net/?f=%280%2C0%29)