Solve 3x^2-2root2-2root3

Question

Find the roots

x_{1} = - \frac{6 2 + 6 3}{3}, x_{2} = \frac{6 2 + 6 3}{3}

Alternative Form

x_{1} \approx - 1.448278, x_{2} \approx 1.448278

Evaluate

3 x^{2} - 22 - 23

To find the roots of the expression,set the expression equal to 0

3 x^{2} - 22 - 23 = 0

Move the constant to the right-hand side and change its sign

3 x^{2} = 0 + 22 + 23

Removing 0 doesn't change the value,so remove it from the expression

3 x^{2} = 22 + 23

Divide both sides

\frac{3 x ^{2}}{3} = \frac{2 2 + 2 3}{3}

Divide the numbers

x^{2} = \frac{2 2 + 2 3}{3}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm \frac{2 2 + 2 3}{3}

Simplify the expression

More Steps

Evaluate

\frac{2 2 + 2 3}{3}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{2 2 + 2 3}{3}

Multiply by the Conjugate

\frac{2 2 + 2 3 \times 3}{3 \times 3}

Multiply the numbers

More Steps

Evaluate

22 + 23 \times 3

The product of roots with the same index is equal to the root of the product

(22 + 23) \times 3

Calculate the product

62 + 63

\frac{6 2 + 6 3}{3 \times 3}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{6 2 + 6 3}{3}

x = \pm \frac{6 2 + 6 3}{3}

Separate the equation into 2 possible cases

x = \frac{6 2 + 6 3}{3} x = - \frac{6 2 + 6 3}{3}

Solution

x_{1} = - \frac{6 2 + 6 3}{3}, x_{2} = \frac{6 2 + 6 3}{3}

Alternative Form

x_{1} \approx - 1.448278, x_{2} \approx 1.448278

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