Solve 73x^6-3 - ScanMath

Question

Find the roots

x_{1} = - \frac{6 3 \times 7 3 ^{5}}{73}, x_{2} = \frac{6 3 \times 7 3 ^{5}}{73}

Alternative Form

x_{1} \approx - 0.587444, x_{2} \approx 0.587444

Evaluate

73 x^{6} - 3

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

73 x^{6} - 3 = 0

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

73 x^{6} = 0 + 3

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

73 x^{6} = 3

Divide both sides

\frac{73 x ^{6}}{73} = \frac{3}{73}

Divide the numbers

x^{6} = \frac{3}{73}

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

x = \pm 6 \frac{3}{73}

Simplify the expression

More Steps

Evaluate

6 \frac{3}{73}

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

\frac{6 3}{6 73}

Multiply by the Conjugate

\frac{6 3 \times 6 7 3 ^{5}}{6 73 \times 6 7 3 ^{5}}

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

\frac{6 3 \times 7 3 ^{5}}{6 73 \times 6 7 3 ^{5}}

Multiply the numbers

More Steps

Evaluate

673 \times 6 7 3^{5}

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

6 73 \times 7 3^{5}

Calculate the product

6 7 3^{6}

Reduce the index of the radical and exponent with 6

73

\frac{6 3 \times 7 3 ^{5}}{73}

x = \pm \frac{6 3 \times 7 3 ^{5}}{73}

Separate the equation into 2 possible cases

x = \frac{6 3 \times 7 3 ^{5}}{73} x = - \frac{6 3 \times 7 3 ^{5}}{73}

Solution

x_{1} = - \frac{6 3 \times 7 3 ^{5}}{73}, x_{2} = \frac{6 3 \times 7 3 ^{5}}{73}

Alternative Form

x_{1} \approx - 0.587444, x_{2} \approx 0.587444

Show Solution