Answer: x = 2 , y = 5
Step-by-step explanation:
10x - 2y = 24 ..................... equation 1
6x + 2y = 8 ........................ equation 2
solving the system of linear equation by elimination method , add equation 1 and 2
16x = 32
divide through by 16
x = 2
substitute x = 2 into equation 1 to find the value of y
10(2) - 2y = 2y
20 - 2y = 2y
20 = 4y
y = 5
Solution :
Given
![$f(x)=x^3-x-1, x_1=1$](https://tex.z-dn.net/?f=%24f%28x%29%3Dx%5E3-x-1%2C%20x_1%3D1%24)
![$f'(x)=3x^2-1$](https://tex.z-dn.net/?f=%24f%27%28x%29%3D3x%5E2-1%24)
Let the initial approximation is ![$x_1 =1$](https://tex.z-dn.net/?f=%24x_1%20%3D1%24)
So by Newton's method, we get
![$x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)},n=1,2,...$](https://tex.z-dn.net/?f=%24x_%7Bn%2B1%7D%3Dx_n-%5Cfrac%7Bf%28x_n%29%7D%7Bf%27%28x_n%29%7D%2Cn%3D1%2C2%2C...%24)
![$x_2=x_1-\frac{f(x_1)}{f'(x_1)}=1-\frac{1^3-1-1}{3(1)^2-1}=1.5$](https://tex.z-dn.net/?f=%24x_2%3Dx_1-%5Cfrac%7Bf%28x_1%29%7D%7Bf%27%28x_1%29%7D%3D1-%5Cfrac%7B1%5E3-1-1%7D%7B3%281%29%5E2-1%7D%3D1.5%24)
![$x_3=1.5-\frac{(1.5)^3-1.5-1}{3(1.5)^2-1}=1.34782608$](https://tex.z-dn.net/?f=%24x_3%3D1.5-%5Cfrac%7B%281.5%29%5E3-1.5-1%7D%7B3%281.5%29%5E2-1%7D%3D1.34782608%24)
![$x_4=1.34782608-\frac{(1.34782608)^3-1.34782608-1}{3(1.34782608)^2-1}=1.32520039$](https://tex.z-dn.net/?f=%24x_4%3D1.34782608-%5Cfrac%7B%281.34782608%29%5E3-1.34782608-1%7D%7B3%281.34782608%29%5E2-1%7D%3D1.32520039%24)
![$x_5=1.32520039-\frac{(1.32520039)^3-1.32520039-1}{3(1.32520039)^2-1}=1.32471817$](https://tex.z-dn.net/?f=%24x_5%3D1.32520039-%5Cfrac%7B%281.32520039%29%5E3-1.32520039-1%7D%7B3%281.32520039%29%5E2-1%7D%3D1.32471817%24)
![$x_6=1.32471817-\frac{(1.32471817)^3-1.32471817-1}{3(1.32471817)^2-1}=1.32471795$](https://tex.z-dn.net/?f=%24x_6%3D1.32471817-%5Cfrac%7B%281.32471817%29%5E3-1.32471817-1%7D%7B3%281.32471817%29%5E2-1%7D%3D1.32471795%24)
are identical up to eight decimal places.
The approximate real root is x ≈ 1.32471795
∴ x = 1.32471795
Answer:
![hj = 11](https://tex.z-dn.net/?f=hj%20%3D%2011)
Step-by-step explanation:
(Given)
Answer:
its the last choice
Step-by-step explanation: