Can A very smart mathematician help me out pls!!! pls pls ...?

Question

I don't know how to use the symbol on the key board so i'm using words.
sovle and explain

1) x+1=9x(cube) + 9x(square)

2) x(cube)= 4x




I promise you 10 points!!

Answer 1

here's how to write the problem with your keyboard:
1) x+1= 9x^3 + 9x^2
2) x^3 = 4x

here's how to solve number 1:

x+1=9x^3 + 9x^2
put everything on the same side of the equal sign and set it to zero:
9x^3 + 9x^2 -x -1 = 0
factor the equation so you can solve the terms for x; first factor out the cube and then the quadratic:
(3x+1)(3x^2+2x+1) = 0
(3x+1)(3x+1)(x+1) = 0
notice how setting the equation to zero allows you to discover the possible values of x; here are the possible values of x in this equation:
3x+1 = 0; 3x = -1; x = -1/3
3x+1 = 0; 3x = -1; x = -1/3
x+1 = 0; x = -1

here's how to solve number 2:

x^3 = 4x
it's the same steps as problem one:
x^3 - 4x = 0
x(x^2 - 4) = 0
x(x-2)(x+2) = 0
these are the possible values of x in this equation:
x = 0
x-2 = 0; so x = 2
x+2 = 0; so x = -2

Answer 2

1) You need to use the principles of synthetic division. First re-write this as

9x^3 + 9x^2 - x - 1 =0

Any rational root of this equation will be of the form a/b where a is a factor of the 0th term (1) and b is a factor of the nth term (9). This makes the possibilities +/- 1, +/- 1/3 and +/- 1/9. Let's try -1/3 or 3x+1. (Use synthetic division on scratch paper by computer...) Yep, that works. (3x+1)(3x^2+2x-1) is the same as above, so one solution is -1/3. Next factor 3x^2+2x-1 into (3x-1)(x+1). The last two answers are 1/3 and -1.

2) Rewrite to x^3 - 4x=0. Factor to x(x^2-4)=0 then to x(x-2)(x+2)=0. The solutions are 0, 2 and -2

Answer 3

1) x= 1/3

2) x=2

Answer 4

x+1= 9x^3+9x^2 ^ means exponents.
9x^3+9x^2-x-1=0 let Y=9x^3+9x^2-x-1
dY/dx=27x^2+18x-1, 27x^2+18x-1 is equal to zero when dY/dx is stationary. then d^2Y/dx^2= 27x+18
then
x= 1/3 and -1 when dY/dx is equal to zero. thus 1/3 and -1are minimum value and maximum value of this equation.
this problem can be solved by CALCULUS.
2) x^3=4x , x^2=4 ,thus x= +2 and -2

Answer 5

1) x = 1

2) x = 2

* for number 1, just keep on regrouping the similar variables, multiply each time to get rid of cube and spuares

Answer 6

1. x = -1

(-1) + 1 = 9 * (-1)^3 + 9 * (-1)^2

-1 + 1 = -9 + 9

0 = 0

2. x = 2

x^3 = 4x

x^2 = 4

x=2

Answer 7

2) x^3=4x
x^3 - 4x = 0
x (x^2 - 4) = 0
x=0 and x^2 - 4=0
x^2=4
x= + and - 2

Answer 8

the answer for #2 is 2

Answer 9

1)

oups ... sorry for the first answer, i'm french and i had think that the term 'square' means '4' ....


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2)

x^3 = 4x

x^2 = 4

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x = {-2 ; 2}

Answer 10

x=root4 (2) from second equation

then substitute root4 (2) into x in first equation