Question

3x в 6 +6x в 4 - x во 2 -2=0

Answer 1

$3x^6+6x^4-x^2-2=0\\\\3x^4(x^2+2)-(x^2+2)=0\\\\(x^2+2)(3x^4-1)=0\\\\x^2+2\ne 0\; ,\; \; (x^2+2>0)\; \\\\3x^4-1=0\; \; \to \; \; (\sqrt3x^2-1)(\sqrt3x^2+1)=0\\\\\sqrt3x^2+1\ne 0\; \; ,\; \; (\sqrt3x^2+1>0)\; \; ,\\\\\sqrt3x^2-1=0\; \; \to \; \; (\sqrt[4]3x-1)(\sqrt[4]3x+1)=0\\\\x_1=\frac{1}{\sqrt[4]3}\; ,\; \; x_2=-\frac{1}{\sqrt[4]3}$

Answer 2

To solve the quadratic equation, we need to set it equal to zero and then use the quadratic formula to find the values of "x". The given equation is:

3x^2 + 6x - x^2 - 2 = 0

First, let's combine the like terms:

(3x^2 - x^2) + 6x - 2 = 0

Now, simplify:

2x^2 + 6x - 2 = 0

Now, we can use the quadratic formula to find the values of "x":

The quadratic formula is given as:

x = (-b ± √(b^2 - 4ac)) / 2a

For our equation, a = 2, b = 6, and c = -2.

Now, plug the values into the formula:

x = ( -6 ± √(6^2 - 42(-2)) ) / 2*2

x = ( -6 ± √(36 + 16) ) / 4

x = ( -6 ± √52 ) / 4

x = ( -6 ± 2√13 ) / 4

Now, simplify:

x = (-3 ± √13) / 2

So, the two solutions for "x" are:

1. x = (-3 + √13) / 2
2. x = (-3 - √13) / 2