SOLUTION: x^4 + radical 3 * x^2 - 3 = 0
Algebra.Com
Question 352923: x^4 + radical 3 * x^2 - 3 = 0
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
The key to making this problem solvable is to recognize that the exponent on is twice as bug as the exponent on . This makes your equation in "quadratic form" for . So we can use techniques for solving quadratic equations to solve for !
To make this process clearer, I am going to use a temporary variable. Let q = . Then . Substituting these into the equation we get:
This is clearly a quadratic equation. With the square root in there, factoring will not be easy. So we'll use the Quadratic formula:
Simplifying:
In long form:
or
This is a solution for q. But we want a solution for x. So we substitute back in for q:
or
Looking at the second equation above we see that the fraction is negative. But a negative numbers cannot be equal to something squared, like ! So unless you are looking for complex solutions, too, there are no solutions to the second equation. We are left with just the first equation:
To solve for x we just find the square root of each side:
(Note: The zero is unnecessary mathematically. But Algebra.com's software will not let me use the "plus or minus" symbol without a number in front of it.)
In long form:
or
Eventually, after doing several of these "quadratic form"-type equations, you will be able to do these problems without a temporary variable. IOW, you will be able to straight from
to
RELATED QUESTIONS
(1-radical 2) (4+3 radical 5)
and
radical x+3= radical... (answered by stanbon)
RADICAL X - 3... (answered by algebrahouse.com)
Please help me solve this system:
x radical 2 + y radical 3 = 0
3x radical 3 - 5y... (answered by greenestamps)
2 radical 5 = 3 radical... (answered by ewatrrr)
solve for x: 3 divided by radical 2-x =... (answered by rfadrogane)
Write expression in radical form... (answered by Tatiana_Stebko)
Find the real solutions of the radical equation.
x^(3/4) - 9[x^(1/4)] =... (answered by josgarithmetic)
(rs) radical sign... (answered by Cintchr)
radical X + 3 = radical... (answered by checkley71)