Solve g^46-10-1 - ScanMath

Question

Simplify the expression

6 g^{4} - 11

Evaluate

g^{4} \times 6 - 10 - 1

Use the commutative property to reorder the terms

6 g^{4} - 10 - 1

Solution

6 g^{4} - 11

Show Solution

g_{1} = - \frac{4 2376}{6}, g_{2} = \frac{4 2376}{6}

Alternative Form

g_{1} \approx - 1.163618, g_{2} \approx 1.163618

Evaluate

g^{4} \times 6 - 10 - 1

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

g^{4} \times 6 - 10 - 1 = 0

Use the commutative property to reorder the terms

6 g^{4} - 10 - 1 = 0

Subtract the numbers

6 g^{4} - 11 = 0

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

6 g^{4} = 0 + 11

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

6 g^{4} = 11

Divide both sides

\frac{6 g ^{4}}{6} = \frac{11}{6}

Divide the numbers

g^{4} = \frac{11}{6}

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

g = \pm 4 \frac{11}{6}

Simplify the expression

More Steps

Evaluate

4 \frac{11}{6}

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

\frac{4 11}{4 6}

Multiply by the Conjugate

\frac{4 11 \times 4 6 ^{3}}{4 6 \times 4 6 ^{3}}

Simplify

\frac{4 11 \times 4 216}{4 6 \times 4 6 ^{3}}

Multiply the numbers

More Steps

Evaluate

411 \times 4216

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

4 11 \times 216

Calculate the product

42376

\frac{4 2376}{4 6 \times 4 6 ^{3}}

Multiply the numbers

More Steps

Evaluate

46 \times 4 6^{3}

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

4 6 \times 6^{3}

Calculate the product

4 6^{4}

Reduce the index of the radical and exponent with 4

6

\frac{4 2376}{6}

g = \pm \frac{4 2376}{6}

Separate the equation into 2 possible cases

g = \frac{4 2376}{6} g = - \frac{4 2376}{6}

Solution

g_{1} = - \frac{4 2376}{6}, g_{2} = \frac{4 2376}{6}

Alternative Form

g_{1} \approx - 1.163618, g_{2} \approx 1.163618

Show Solution