На прямой m лежат точки m n k, причём mn=85 мм nk=1, 15дм какой может быть длина отрезка mk в сантиметрах

Mn=85 мм= 8.5 см ;   nk=1,15дм=11.5 cмесли точка n лежит между м и к, то мк = mn+nk= 8.5+11.5 =20 смесли точка m лежит между k и n, то мк = nk-nm= 11.5-8.5 = 3  см

Simplifying

4x3 + -81x = 0

Reorder the terms:

-81x + 4x3 = 0

Solving

-81x + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.

x(-81 + 4x2) = 0

Factor a difference between two squares.

x((9 + 2x)(-9 + 2x)) = 0

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve:

Simplifying

x = 0

Solving

x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying

x = 0

Subproblem 2

Set the factor '(9 + 2x)' equal to zero and attempt to solve:

Simplifying

9 + 2x = 0

Solving

9 + 2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-9' to each side of the equation.

9 + -9 + 2x = 0 + -9

Combine like terms: 9 + -9 = 0

0 + 2x = 0 + -9

2x = 0 + -9

Combine like terms: 0 + -9 = -9

2x = -9

Divide each side by '2'.

x = -4.5

Simplifying

x = -4.5

Subproblem 3

Set the factor '(-9 + 2x)' equal to zero and attempt to solve:

Simplifying

-9 + 2x = 0

Solving

-9 + 2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '9' to each side of the equation.

-9 + 9 + 2x = 0 + 9

Combine like terms: -9 + 9 = 0

0 + 2x = 0 + 9

2x = 0 + 9

Combine like terms: 0 + 9 = 9

2x = 9

Divide each side by '2'.

x = 4.5

Simplifying

x = 4.5

Solution

x = {0, -4.5, 4.5}

1) r^3*s^3  *  (  s  +  r) 2)  5a^3*x*(  4  -  3ax) 3)  (x  -  3)*(x  +  3) 4)  (  1  -  5y)*(1  +  5y) 5)  (3x  -  2x^2)  +  (  3y  -  2xy)  =  x*(3 -  2x)  +  y*(3  -  2x)  =  (  3  -  2x  )  *  (  x  +  y  ) 6) (20z^2k  -  5k)  +  (2z  +  1)  =  5k*(4z^2  -  1)  +  (2z  +  1)  =  5k*(2z  -  1)*(2z  +  1)  + +  (2z  +  1)  =  (2z  +  1)*(2z  +1)*(2z  -  1)*5k 7) 16t^2 +  s^2*(8t  +  s^2)  =  2*(8t  +  s^2)*(8t  +  s^2) 8) b^4  -  16c*(b^2  +  4c)  =  (b^2  -  4c)*(b^2  +  4c)