Answer:
The solved expression is
and ![x=3-\sqrt{2}](https://tex.z-dn.net/?f=x%3D3-%5Csqrt%7B2%7D)
Therefore ![x=3\pm\sqrt{2}](https://tex.z-dn.net/?f=x%3D3%5Cpm%5Csqrt%7B2%7D)
Step-by-step explanation:
Given quadratic equation is ![x^2-6x+7=0](https://tex.z-dn.net/?f=x%5E2-6x%2B7%3D0)
To solve the given equation by using completing the square :
![x^2-6x+7=0](https://tex.z-dn.net/?f=x%5E2-6x%2B7%3D0)
Rewritting the above equation as below :
![x^2-6x+7+2-2=0](https://tex.z-dn.net/?f=x%5E2-6x%2B7%2B2-2%3D0)
![(x^2-6x+7+2)-2=0](https://tex.z-dn.net/?f=%28x%5E2-6x%2B7%2B2%29-2%3D0)
![(x^2-6x+9)-2=0](https://tex.z-dn.net/?f=%28x%5E2-6x%2B9%29-2%3D0)
![(x^2-6x+3^2)-2=0](https://tex.z-dn.net/?f=%28x%5E2-6x%2B3%5E2%29-2%3D0)
( it is of the form of
heere a=x and b=3 )
![(x-3)^2-2=0](https://tex.z-dn.net/?f=%28x-3%29%5E2-2%3D0)
![(x-3)^2=2](https://tex.z-dn.net/?f=%28x-3%29%5E2%3D2)
Taking square root on both sides we get
![\sqrt{(x-3)^2}=\pm\sqrt{2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x-3%29%5E2%7D%3D%5Cpm%5Csqrt%7B2%7D)
![x-3=\pm\sqrt{2}](https://tex.z-dn.net/?f=x-3%3D%5Cpm%5Csqrt%7B2%7D)
![x=\pm\sqrt{2}+3](https://tex.z-dn.net/?f=x%3D%5Cpm%5Csqrt%7B2%7D%2B3)
![x=3\pm\sqrt{2}](https://tex.z-dn.net/?f=x%3D3%5Cpm%5Csqrt%7B2%7D)
Therefore
and ![x=3-\sqrt{2}](https://tex.z-dn.net/?f=x%3D3-%5Csqrt%7B2%7D)
Answer:
27
Step-by-step explanation:
The answer is 27, because 9 x 3 = 27 and the smallest number that is the same is 27.
Hope this helps!
Answer:
Theoretical probability is a method is found by dividing the number of favorable outcomes by the total possible outcomes.
Step-by-step explanation:
The answer to this equation is 8^5
To prove: ![\cot x+\tan x=\sec x\csc x](https://tex.z-dn.net/?f=%5Ccot%20x%2B%5Ctan%20x%3D%5Csec%20x%5Ccsc%20x)
where ![x\neq \dfrac{\pi}{2}(2n-1)](https://tex.z-dn.net/?f=x%5Cneq%20%5Cdfrac%7B%5Cpi%7D%7B2%7D%282n-1%29)
Using trigonometry formula:
![\cot x=\dfrac{\cos x}{\sin x}](https://tex.z-dn.net/?f=%5Ccot%20x%3D%5Cdfrac%7B%5Ccos%20x%7D%7B%5Csin%20x%7D)
![\tan x=\dfrac{\sin x}{\cos x}](https://tex.z-dn.net/?f=%5Ctan%20x%3D%5Cdfrac%7B%5Csin%20x%7D%7B%5Ccos%20x%7D)
![\sec x=\dfrac{1}{\cos x}](https://tex.z-dn.net/?f=%5Csec%20x%3D%5Cdfrac%7B1%7D%7B%5Ccos%20x%7D)
![\csc x=\dfrac{1}{\sin x}](https://tex.z-dn.net/?f=%5Ccsc%20x%3D%5Cdfrac%7B1%7D%7B%5Csin%20x%7D)
Taking Left hand side
![\Rightarrow \dfrac{\cos x}{\sin x}+\dfrac{\sin x}{\cos x}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cdfrac%7B%5Ccos%20x%7D%7B%5Csin%20x%7D%2B%5Cdfrac%7B%5Csin%20x%7D%7B%5Ccos%20x%7D)
![\Rightarrow \dfrac{\cos^2 x+\sin^2x}{\sin x\cos x}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cdfrac%7B%5Ccos%5E2%20x%2B%5Csin%5E2x%7D%7B%5Csin%20x%5Ccos%20x%7D)
![\because \cos^2 x+\sin^2x=1](https://tex.z-dn.net/?f=%5Cbecause%20%5Ccos%5E2%20x%2B%5Csin%5E2x%3D1)
Hence proved