Anyone know what a^2-2a-8=0 is
1 answer:
You might be interested in
Hi!
We are given the information found in the picture below.
Note: The directions aren't correct, but the triangle works for this problem.
The "direct path" is the hypotenuse of this triangle.
To find this, we use the Pythagorean Theorem, where and
are 2 legs of the triangle, and
is the hypotenuse, aka the longest side of any triangle:
We know and
and want
Therefore, is approximately
Just put the coefients in to a matrix
1x-6y-3z=4
-2x+0y-3z=-8
-2x+2y-3z=-14
![\left[\begin{array}{ccc}1&-6&-3|4\\-2&0&-3|-8\\-2&2&-3|-14\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26-6%26-3%7C4%5C%5C-2%260%26-3%7C-8%5C%5C-2%262%26-3%7C-14%5Cend%7Barray%7D%5Cright%5D%20)
mulstiply 2nd row by -1 and add to 3rd
![\left[\begin{array}{ccc}1&-6&-3|4\\-2&0&-3|-8\\0&2&0|-6\end{array}\right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26-6%26-3%7C4%5C%5C-2%260%26-3%7C-8%5C%5C0%262%260%7C-6%5Cend%7Barray%7D%5Cright%5D)
divde last row by 2
![\left[\begin{array}{ccc}1&-6&-3|4\\-2&0&-3|-8\\0&1&0|-3\end{array}\right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26-6%26-3%7C4%5C%5C-2%260%26-3%7C-8%5C%5C0%261%260%7C-3%5Cend%7Barray%7D%5Cright%5D)
multiply 2rd row by 6 and add to top one
![\left[\begin{array}{ccc}1&0&-3|-14\\-2&0&-3|-8\\0&1&0|-3\end{array}\right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%26-3%7C-14%5C%5C-2%260%26-3%7C-8%5C%5C0%261%260%7C-3%5Cend%7Barray%7D%5Cright%5D)
multiply 1st row by -1 and add to 2nd
![\left[\begin{array}{ccc}1&0&-3|-14\\-3&0&0|6\\0&1&0|-3\end{array}\right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%26-3%7C-14%5C%5C-3%260%260%7C6%5C%5C0%261%260%7C-3%5Cend%7Barray%7D%5Cright%5D)
divide 2nd row by -3
![\left[\begin{array}{ccc}1&0&-3|-14\\1&0&0|-2\\0&1&0|-3\end{array}\right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%26-3%7C-14%5C%5C1%260%260%7C-2%5C%5C0%261%260%7C-3%5Cend%7Barray%7D%5Cright%5D)
mulstiply 2nd row by -1 and add to 1st row
![\left[\begin{array}{ccc}0&0&-3|-12\\1&0&0|-2\\0&1&0|-3\end{array}\right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%260%26-3%7C-12%5C%5C1%260%260%7C-2%5C%5C0%261%260%7C-3%5Cend%7Barray%7D%5Cright%5D)
divide 1st row by -3
![\left[\begin{array}{ccc}0&0&1|4\\1&0&0|-2\\0&1&0|-3\end{array}\right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%260%261%7C4%5C%5C1%260%260%7C-2%5C%5C0%261%260%7C-3%5Cend%7Barray%7D%5Cright%5D)
rerange
![\left[\begin{array}{ccc}1&0&0|-2\\0&1&0|-3\\0&0&1| 4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%260%7C-2%5C%5C0%261%260%7C-3%5C%5C0%260%261%7C%204%5Cend%7Barray%7D%5Cright%5D)
x=-2
y=-3
z=4
(x,y,z)
(-2,-3,4)
B is answer
1x-6y-3z=4
-2x+0y-3z=-8
-2x+2y-3z=-14
mulstiply 2nd row by -1 and add to 3rd
divde last row by 2
multiply 2rd row by 6 and add to top one
multiply 1st row by -1 and add to 2nd
divide 2nd row by -3
mulstiply 2nd row by -1 and add to 1st row
divide 1st row by -3
rerange
x=-2
y=-3
z=4
(x,y,z)
(-2,-3,4)
B is answer