CPhill

Rearrange as

3x^2 - 16x + 17  = 0

ab = 17/3   →  2ab  = 34/3     

 a + b = 16/3      square both sides

 a^2 + 2ab + b^2 = 256/9

 a^2  + 34/3 + b^2  = 256/9

 a^2 + b^2  = 154/9

ab = 17/3

(ab)^2 = 289/9

a^2 * b^2  = 289 / 9

The polynomial is

x^2  - (154/9)x + 289 / 9

                        3x^2 -  x  + 4

x^2 + 4x - 2  [  3x^4 + 11x^3  + kx^2 + 18x - 8 ]

                        3x^4 + 12x^3 - 6x^2

                      ___________________________

                                   -1x^3 + (k + 6)x^2 + 18x

                                   -1x^3  -  4x^2   + 2x

                                __________________________

                                                 (k + 10)x^2 + 16x - 8

                                                      4x^2      + 16x  -8

                                                 _____________________

                                                   (k + 6) x^2

k + 6  =  0

k =  -6

https://web2.0calc.com/questions/help-counting_95222

There is a (messy) algebraic solution, but a graph works better

The left hand side is  represented by the lower graph and the right hand  side is  represented by the upper graph..

The graphs do not intersect, so there is no "c"  that makes the two sides of the equations equal....

https://web2.0calc.com/questions/let-x-y-and-z-be-nonzero-real-numbers-find-all-possible

Can't be done with 20 yellow tiles

The center tile is  yellow.....this leaves 19 yellow tiles that must be distributed symmetrically along each diagonal....but this means that each half-diagonal would have to contain 19/4 tiles....but 19/4  isn't an integer

After n steps, the number of lattice points (points with integer coordinates) he could reach  = (n + 1)^2

So.... (2 + 1)^2  = 3^2  =   9 points

 2x - 5 <= -x + 12 - 7x + 18

Rearrange  as

10x <= 35

x <= 35  / 10

x <= 7 /  2

Rearrange L1  as

-3y = -11x - 14

Slope of L1   = 11/3

Slope of a perpendicular line  = -3/11

L2  equation L

y = (-3/11) (x - 5) - 6

y = (-3/11)x + 15/11 - 6

y = (-3/11)x + 15/11 - 66/11

y = (-3/11)x - 51/11

Rearrange the given equation as

18y = -5x - 8

The slope of  a parallel line is   -5/18

The equation of a parallel line  through  (-1,8)  is

y =(-5/18)(x + 1) + 8

y = (-5/18)x  - 5/18 + 8

y = (-5/18)x + 139/18

18y = -5x  + 139

5x + 18y  = 139