Solve x^3 x-3x^2-3 - ScanMath

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Question

Simplify the expression

x^{4} - 3 x^{2} - 3

Show Solution

Find the roots

x_{1} = - \frac{6 + 2 21}{2}, x_{2} = \frac{6 + 2 21}{2}

Alternative Form

x_{1} \approx - 1.947123, x_{2} \approx 1.947123

Evaluate

x^{3} \times x - 3 x^{2} - 3

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

x^{3} \times x - 3 x^{2} - 3 = 0

Multiply the terms

More Steps

x^{4} - 3 x^{2} - 3 = 0

Solve the equation using substitution t = x^{2}

t^{2} - 3 t - 3 = 0

Substitute a= 1,b= - 3 and c= - 3 into the quadratic formula t = \frac{- b \pm b ^{2} - 4 a c}{2 a}

t = \frac{3 \pm ( - 3 ) ^{2} - 4 ( - 3 )}{2}

Simplify the expression

More Steps

t = \frac{3 \pm 21}{2}

Separate the equation into 2 possible cases

t = \frac{3 + 21}{2} t = \frac{3 - 21}{2}

Substitute back

x^{2} = \frac{3 + 21}{2} x^{2} = \frac{3 - 21}{2}

Solve the equation for x

More Steps

x = \frac{6 + 2 21}{2} x = - \frac{6 + 2 21}{2} x^{2} = \frac{3 - 21}{2}

Solve the equation for x

More Steps

x = \frac{6 + 2 21}{2} x = - \frac{6 + 2 21}{2} x = \frac{2 21 - 6}{2} i x = - \frac{2 21 - 6}{2} i

Calculate

x = \frac{6 + 2 21}{2} x = - \frac{6 + 2 21}{2}

Solution

x_{1} = - \frac{6 + 2 21}{2}, x_{2} = \frac{6 + 2 21}{2}

Alternative Form

x_{1} \approx - 1.947123, x_{2} \approx 1.947123

Show Solution