Question

MEDAL+Fan+1 Great Fan Testimonial will be given!

Solve x^4 < 36x^2 Please!

Answer 1

x^4-36x^2<0
x^2(x^2-36)<0
for to be less than 0 , have to be x^2<36
so -6<x<6

Answer 2

and then what skullpatrol?

Answer 3

I gave you the answer already

Answer 4

the skull patrol is correct but if u give any value to x you will get hte right answere @Christos

Answer 5

yes skullpartol x^2 is always positive, what can I do then? Do you know?

Answer 6

x^(4)<36x^(2)

Since 36x^(2) contains the variable to solve for, move it to the left-hand side of the inequality by subtracting 36x^(2) from both sides.
x^(4)-36x^(2)<0

Factor out the GCF of x^(2) from the expression x^(4).
x^(2)(x^(2))-36x^(2)<0

Factor out the GCF of x^(2) from the expression -36x^(2).
x^(2)(x^(2))+x^(2)(-36)<0

Factor out the GCF of x^(2) from x^(4)-36x^(2).
x^(2)(x^(2)-36)<0

The binomial can be factored using the difference of squares formula, because both terms are perfect squares. The difference of squares formula is a^(2)-b^(2)=(a-b)(a+b).
x^(2)(x-6)(x+6)<0

Set the single term factor on the left-hand side of the inequality equal to 0 to find the critical points.
x^(2)=0

Take the square root of both sides of the equation to eliminate the exponent on the left-hand side.
x=\~(0)

Pull all perfect square roots out from under the radical. In this case, remove the 0 because it is a perfect square.
x=\0

\0 is equal to 0.
x=0

Set each of the factors of the left-hand side of the inequality equal to 0 to find the critical points.
x-6=0_x+6=0

Since -6 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 6 to both sides.
x=6_x+6=0

Set each of the factors of the left-hand side of the inequality equal to 0 to find the critical points.
x=6_x+6=0

Since 6 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 6 from both sides.
x=6_x=-6

To find the solution set that makes the expression less than 0, break the set into real number intervals based on the values found earlier.
x<-6_-6<x<0_0<x<6_6<x

Determine if the given interval makes each factor positive or negative. If the number of negative factors is odd, then the entire expression over this interval is negative. If the number of negative factors is even, then the entire expression over this interval is positive.
x<-6 makes the expression negative_-6<x<0 makes the expression positive_0<x<6 makes the expression negative_6<x makes the expression positive

Since this is a 'less than 0' inequality, all intervals that make the expression negative are part of the solution.
x<-6 or 0<x<6