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

The solutions are x =
,
and

User COMisHARD
by
6.7k points

2 Answers

2 votes

Answer:


-(1)/(2),0,(3)/(2)

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=(3)/(2)=1.5


2x=-3 \implies x=-(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=(1)/(2)=0.5


2x+1=0


2x=-1 \implies x=-(1)/(2)=-0.5

When we substitute x=
(1)/(2)


4((1)/(2))^3-(5)/(2)=(1)/(2)-(5)/(2)=(1-5)/(2)=-2


\mid 4((1)/(2))\mid=2


-2\\eq 2

Hence,
(1)/(2) is a not solution of given equation.

When substitute
x=(-3)/(2)


4((-3)/(2))^3+(15)/(2)=(-27)/(2)+(15)/(2)=(-27+15)/(2)=-6


\mid 4(-(3)/(2)\mid=6


-6\\eq 6

Hence,
(-3)/(2) is not a solution of given equation.

Substitute x=
-(1)/(2) in the given equation


4(-(1)/(2))^3+(5)/(2)=-(1)/(2)+(5)/(2)=2


\mid 4(-(1)/(2))\mid=2


2=2

Hence,
-(1)/(2) is a solution of given equation.

Substitute
x=(3)/(2) in the given equation


4((3)/(2))^3-(15)/(2)=(27-15)/(2)=6


\mid 4((3)/(2))\mid =6


6=6

Hence,
(3)/(2) is a solution of given equation.

Answer:
-(1)/(2),0,(3)/(2)

User Savvas Dalkitsis
by
7.3k points
3 votes

Answer:

-1/2 , 0 , 3/2

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 = (9)/(4) \\√(x^2)=\sqrt{(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 = (1)/(4) \\√(x^2)=\sqrt{(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((1)/(2))^3 - 5((1)/(2)) = |4 * (1)/(2)|\\ &nbsp; 4 * ((1)/(8)) - (5)/(2) = |2|\\ -2 = 2\\Put\ x=-(3)/(2) \\4((-3)/(2))^3 - 5((-3)/(2)) = |4 * (-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 ..

User Utkarsh Pandey
by
6.6k points