The answer to this problem is 18
You have the slope and you have two points, so you can use the slope equation to find x.

So your answer is x = 8.
Answer:
The statement is true is for any
.
Step-by-step explanation:
First, we check the identity for
:



The statement is true for
.
Then, we have to check that identity is true for
, under the assumption that
is true:
![(1^{2}+2^{2}+3^{2}+...+k^{2}) + [2\cdot (k+1)-1]^{2} = \frac{(k+1)\cdot [2\cdot (k+1)-1]\cdot [2\cdot (k+1)+1]}{3}](https://tex.z-dn.net/?f=%281%5E%7B2%7D%2B2%5E%7B2%7D%2B3%5E%7B2%7D%2B...%2Bk%5E%7B2%7D%29%20%2B%20%5B2%5Ccdot%20%28k%2B1%29-1%5D%5E%7B2%7D%20%3D%20%5Cfrac%7B%28k%2B1%29%5Ccdot%20%5B2%5Ccdot%20%28k%2B1%29-1%5D%5Ccdot%20%5B2%5Ccdot%20%28k%2B1%29%2B1%5D%7D%7B3%7D)
![\frac{k\cdot (2\cdot k -1)\cdot (2\cdot k +1)}{3} +[2\cdot (k+1)-1]^{2} = \frac{(k+1)\cdot [2\cdot (k+1)-1]\cdot [2\cdot (k+1)+1]}{3}](https://tex.z-dn.net/?f=%5Cfrac%7Bk%5Ccdot%20%282%5Ccdot%20k%20-1%29%5Ccdot%20%282%5Ccdot%20k%20%2B1%29%7D%7B3%7D%20%2B%5B2%5Ccdot%20%28k%2B1%29-1%5D%5E%7B2%7D%20%3D%20%5Cfrac%7B%28k%2B1%29%5Ccdot%20%5B2%5Ccdot%20%28k%2B1%29-1%5D%5Ccdot%20%5B2%5Ccdot%20%28k%2B1%29%2B1%5D%7D%7B3%7D)
![\frac{k\cdot (2\cdot k -1)\cdot (2\cdot k +1)+3\cdot [2\cdot (k+1)-1]^{2}}{3} = \frac{(k+1)\cdot [2\cdot (k+1)-1]\cdot [2\cdot (k+1)+1]}{3}](https://tex.z-dn.net/?f=%5Cfrac%7Bk%5Ccdot%20%282%5Ccdot%20k%20-1%29%5Ccdot%20%282%5Ccdot%20k%20%2B1%29%2B3%5Ccdot%20%5B2%5Ccdot%20%28k%2B1%29-1%5D%5E%7B2%7D%7D%7B3%7D%20%3D%20%5Cfrac%7B%28k%2B1%29%5Ccdot%20%5B2%5Ccdot%20%28k%2B1%29-1%5D%5Ccdot%20%5B2%5Ccdot%20%28k%2B1%29%2B1%5D%7D%7B3%7D)

![(2\cdot k +1)\cdot [k\cdot (2\cdot k -1)+3\cdot (2\cdot k +1)] = (k+1) \cdot (2\cdot k +1)\cdot (2\cdot k +3)](https://tex.z-dn.net/?f=%282%5Ccdot%20k%20%2B1%29%5Ccdot%20%5Bk%5Ccdot%20%282%5Ccdot%20k%20-1%29%2B3%5Ccdot%20%282%5Ccdot%20k%20%2B1%29%5D%20%3D%20%28k%2B1%29%20%5Ccdot%20%282%5Ccdot%20k%20%2B1%29%5Ccdot%20%282%5Ccdot%20k%20%2B3%29)



Therefore, the statement is true for any
.
First determine the index of the radical
If the index is an even number, set the expression inside the radical greater than or equal to zero.
Solve the equation found above :)
Answer:
..fyjnvcftuukloyrsszxccccccx