Simplifying the equation:
We are given the bi-quadratic equation:
9x⁴-3x²+1
to factorise this equation, we will convert it to a quadratic equation and factor it from there
in the given equation, let x² = y
now, the equation looks like:
9y² - 3y + 1
Finding the Factors (in terms of y):
Using the quadratic formula: x = -b±√(b²-4ac) / 2a
replacing the variables in the equation
y = [-(-3) ± √[(-3)² - 4(9)(1)]]/2(9)
y= [3 ± √-27]/18
y = (1 ± √-3 / 6)
The 2 solutions are:
y = (1 + √-3 / 6) and y = (1 - √-3 / 6)
Finding the values of 'x':
Since y = x²:
x² = (1 + √-3 / 6) and x² = (1 - √-3 / 6)
taking the square root of both sides
x = √(1 + √-3 / 6) and x = √(1 - √-3 / 6)
As we can see, the given equation has complex roots and cannot be simplified further