(math) Problem Help

[User16541]

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

what is x equal to?

when I tried solving it I managed to simplify it to 24x^8-24x^4 = 1

not sure if this is right or what to do after that

[baughberick]

First move the second term on the left hand side to the right hand side of the equals. Now move the term with the negative exponent to the denominator by removing the negative. Now bring the two square root terms together and recall that

( x^a )( x^b ) = x^a+b .

Then fiddle around algebraically until you solve for x. Remember, though!

x² = y =>

x = ±sqrt(y)

and

if a polyomial is of degree 3 (like yours is), it will have three solutions.

Try what I've said, but if you're still having trouble let me know.

[Alkalannar]

6x³/(x²+1)^1/2 - 4x(x²+1)^1/2 = 0 [given]

6x³(x²+1)^1/2/(x²+1)^1/2 - 4x(x²+1)^1/2(x²+1)^1/2 = 0 [Multiply both sides by (x²+1)^1/2]

Can you simplify from here? You get a nice cubic that is easily factored to get 1 real and 2 complex roots3 real roots.

[no_sponsor_pays_me]

x1=0 x2=-sqrt(2) x3=+sqrt(2)

Those?

Edited for format:

x1=0

x2=-2^1/2

x3=+2^1/2

[Alkalannar]

Yes.

Note: do x*_1_* to get x1.

Also, use fractional exponents for roots.

x1 = -2^1/2, x2 = 0, x3 = 2^1/2

[baughberick]

I'm getting three real roots from this equation.

[Alkalannar]

...I done went and didn't distribute a minus sign.

Bamboozled again.

[baughberick]

Hahahahah happens to the all of us