Solve. 25x^4-15x^2+2=0
Substitute u = x^2, and solve
25u^2 -15u +2 = 0
(5u -1)(5u-2) = 0
u = 1/5 or 2/5
x = sqrt u
Take it from there.
To solve the equation 25x^4 - 15x^2 + 2 = 0, we can use a technique called factoring. However, this equation does not easily factor, so we'll use a different method called the quadratic formula.
The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Let's apply this formula to our equation:
For the equation 25x^4 - 15x^2 + 2 = 0, we can see that a = 25, b = -15, and c = 2. Plugging these values into the quadratic formula, we get:
x = (-(-15) ± √((-15)^2 - 4*25*2)) / (2*25)
Simplifying further:
x = (15 ± √(225 - 200)) / 50
= (15 ± √25) / 50
Now, we can simplify the expression inside the square root:
x = (15 ± 5) / 50
This gives us two possible solutions:
1. x = (15 + 5) / 50 = 20 / 50 = 0.4
2. x = (15 - 5) / 50 = 10 / 50 = 0.2
So, the two solutions to the equation 25x^4 - 15x^2 + 2 = 0 are x = 0.4 and x = 0.2.