Question

4x^2/3 + 5x^1/3 - 6 = 0

What is the value of x?

Answer 1

I don't understand why there is only 1 answer....

Answer 2

Let u = x^1/3

Then

4u^2 + 5u - 6 = 0, an equation that you can solve.

Answer 3

apparently the only aswer is 27/64 , but I get -8 as an answer as well

Answer 4

Thanks JamesJ I did that too, I got

u = 3/4
and -2

Answer 5

let u=x^(1/3)
then u^2=x^(2/3)
so we have
4u^2+5u-6=0
to factor we need to find two factors of 4(-6) that have product 4(-6) and sum 5
4(-6)=-12(2)=-3(8)
5=-3+8
so
5u=-3u+8u
replace 5u with -3u+8u in 4u^2+5u-6=0
so we have
4u^2-3u+8u-6=0
now factor by grouping
u(4u-3)+2(4u-3)=0
(4u-3)(u+2)=0
=>
u=3/4 or u=-2
but remember u=x^(1/3)
so we have
x^(1/3)=3/4 or x^(1/3)=-2

raise both sides to the third power
x=(3/4)^3 or x=(-2)^(3)
x=27/64 or x=-8

now we can check both of these by pluggin' them into the original equation
so checking x=-8

4(-8)^(2/3)+5(-8)^(1/3)-6
=
4(-2)^2+5(-2)-6
=
4(4)-10-6
=
16-10-6
=
6-6
=
0
so both sides are 0! YAY!!! x=-8 works!
now let's check x=27/64

4(27/64)^(2/3)+5(27/64)^(1/3)-6
=
4(3/4)^2+5(3/4)-6
=
4(9/16)+15/4-6
=
9/4+15/4-6
=
24/4-6
=
6-6
=0
both sides are zero that means x=27/64 works too!
we have two solutions

Answer 6

THanks soooooooooo much =)) I guess the answer sheet is wrong. I became a fan too :))

Answer 7

ok lol
thanks

Answer 8

does it ask for one solution?

Answer 9

or does it tell you to list all solutions?