Solve (x 1) (x^2) (x^3) (x^4) -3

Question

Simplify the expression

x^{10} - 3

Evaluate

(x \times 1) x^{2} \times x^{3} \times x^{4} - 3

Remove the parentheses

x \times 1 \times x^{2} \times x^{3} \times x^{4} - 3

Solution

More Steps

Evaluate

x \times 1 \times x^{2} \times x^{3} \times x^{4}

Rewrite the expression

x \times x^{2} \times x^{3} \times x^{4}

Multiply the terms with the same base by adding their exponents

x^{1 + 2 + 3 + 4}

Add the numbers

x^{10}

x^{10} - 3

Show Solution

x_{1} = - 103, x_{2} = 103

Alternative Form

x_{1} \approx - 1.116123, x_{2} \approx 1.116123

Evaluate

(x \times 1) (x^{2}) (x^{3}) (x^{4}) - 3

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

(x \times 1) (x^{2}) (x^{3}) (x^{4}) - 3 = 0

Any expression multiplied by 1 remains the same

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

Calculate

x \times x^{2} (x^{3}) (x^{4}) - 3 = 0

Calculate

x \times x^{2} \times x^{3} (x^{4}) - 3 = 0

Calculate

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

Multiply

More Steps

Multiply the terms

x \times x^{2} \times x^{3} \times x^{4}

Multiply the terms with the same base by adding their exponents

x^{1 + 2 + 3 + 4}

Add the numbers

x^{10}

x^{10} - 3 = 0

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

x^{10} = 0 + 3

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

x^{10} = 3

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

x = \pm 103

Separate the equation into 2 possible cases

x = 103 x = - 103

Solution

x_{1} = - 103, x_{2} = 103

Alternative Form

x_{1} \approx - 1.116123, x_{2} \approx 1.116123

Show Solution