6x^4-7x^2+2=0
is it 2^1/2 over 3^1/2
To determine whether 2^(1/2) over 3^(1/2) is a solution to the equation 6x^4-7x^2+2=0, we need to substitute this value into the equation and see if it satisfies it.
First, let's simplify 2^(1/2) over 3^(1/2):
2^(1/2) = sqrt(2) ≈ 1.414
3^(1/2) = sqrt(3) ≈ 1.732
So, 2^(1/2) over 3^(1/2) can be calculated as approximately 1.414 / 1.732 ≈ 0.817.
Now, let's substitute this value, x = 0.817, back into the equation:
6x^4 - 7x^2 + 2 = 0
6(0.817)^4 - 7(0.817)^2 + 2 = 0
0.876 - 4.793 + 2 ≈ -1.917
Since the equation evaluates to approximately -1.917 when x = 0.817, we can conclude that 2^(1/2) over 3^(1/2) is not a solution to the given equation.