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TamB01

TamB01

27.06.2019 •

Mathematics

What are the solutions to the equation 4x 3 - 5x = |4x|? list your answers in increasing order.
the solutions are x =
,
and

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Ответ:

dedgefield

10.03.2022

-1/2 , 0 , 3/2

Step-by-step explanation:

Given equation is:

4x^3-5x = |4x|

We know that $|x|=a\\The\ solution\ will\ be:\\x=a\ and\ x=-a\\$

So, from given equation,we will get two solutions:

$4x^3-5x = 4x\\4x^3-5x-4x=0\\4x^3-9x=0\\x(4x^2-9) = 0\\x = 0\\and\\4x^2-9 = 0\\4x^2=9\\x^2 = \frac{9}{4} \\\sqrt{x^2}=\sqrt{\frac{9}{4} }\\$

x= ±√3/2 , 0

and

$4x^3-5x = -4x\\4x^3-5x+4x=0\\4x^3-x=0\\x(4x^2-1) = 0\\x = 0\\and\\4x^2-1 = 0\\4x^2=1\\x^2 = \frac{1}{4} \\\sqrt{x^2}=\sqrt{\frac{1}{4} }$

x= ±1/2 , 0

We can check that 1/2 and -3/2 do not satisfy the given equation.

$4x^3-5x = |4x|\\Put\ x=1/2\\4(\frac{1}{2})^3 - 5(\frac{1}{2}) = |4 * \frac{1}{2}|\\ 4 * (\frac{1}{8)} - \frac{5}{2} = |2|\\ -2 = 2\\Put\ x=-\frac{3}{2} \\4(\frac{-3}{2})^3 - 5(\frac{-3}{2}) = |4 * \frac{-3}{2}|\\-6 = 6\\$

So, 1/2 and -3/2 will not be the part of the solution ..

So, the solutions in increasing order are:

-1/2 , 0 , 3/2 ..

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Ответ:

artbydi

10.03.2022

$-\frac{1}{2},0,\frac{3}{2}$

Step-by-step explanation:

We are given that an equation

$4x^3-5x=\mid x\mid$

We have to find the solution of given equation and arrange the solution in increasing order.

4x^3-5x=4x when x >0

and 4x^3-5x=-4x when x < 0

because $\mid x\mid =x when x 0$

=-x when x < 0

4x^3-5x-4x=0

4x^3-9x=0

x(4x^2-9)=0

x(2x+3)(2x-3)=0

Using identity a^2-b^2=(a+b)(a-b)

x=0,2x+3=0,2x-3=0

$2x=3\implies x=\frac{3}{2}=1.5$

$2x=-3 \implies x=-\frac{3}{2}=-1.5$

4x^3-5x=-4x=0

4x^3-5x+4x=0

4x^3-x=0

x(4x^2-1)=0

x(2x+1)(2x-1)=0

x=0,2x+1=0

2x-1=0

2x-1=0

$2x=1 \ilmplies x=\frac{1}{2}=0.5$

2x+1=0

$2x=-1 \implies x=-\frac{1}{2}=-0.5$

When we substitute x= $\frac{1}{2}$

$4(\frac{1}{2})^3-\frac{5}{2}=\frac{1}{2}-\frac{5}{2}=\frac{1-5}{2}=-2$

$\mid 4(\frac{1}{2})\mid=2$

$-2\neq 2$

Hence, $\frac{1}{2}$ is a not solution of given equation.

When substitute $x=\frac{-3}{2}$

$4(\frac{-3}{2})^3+\frac{15}{2}=\frac{-27}{2}+\frac{15}{2}=\frac{-27+15}{2}=-6$

$\mid 4(-\frac{3}{2}\mid=6$

$-6\neq 6$

Hence, $\frac{-3}{2}$ is not a solution of given equation.

Substitute x= $-\frac{1}{2}$ in the given equation

$4(-\frac{1}{2})^3+\frac{5}{2}=-\frac{1}{2}+\frac{5}{2}=2$

$\mid 4(-\frac{1}{2})\mid=2$

2=2

Hence, $-\frac{1}{2}$ is a solution of given equation.

Substitute $x=\frac{3}{2}$ in the given equation

$4(\frac{3}{2})^3-\frac{15}{2}=\frac{27-15}{2}=6$

$\mid 4(\frac{3}{2})\mid =6$

6=6

Hence, $\frac{3}{2}$ is a solution of given equation.

$-\frac{1}{2},0,\frac{3}{2}$

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Ответ:

preguntassimples

23.10.2021

275 can be divided by 55

1150 can be divided by 230

plz mark as a brainliest

Step-by-step explanation:

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