Solve 5751a^2-1 - ScanMath

Question

Find the roots

a_{1} = - \frac{71}{639}, a_{2} = \frac{71}{639}

Alternative Form

a_{1} \approx - 0.013186, a_{2} \approx 0.013186

Evaluate

5751 a^{2} - 1

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

5751 a^{2} - 1 = 0

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

5751 a^{2} = 0 + 1

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

5751 a^{2} = 1

Divide both sides

\frac{5751 a ^{2}}{5751} = \frac{1}{5751}

Divide the numbers

a^{2} = \frac{1}{5751}

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

a = \pm \frac{1}{5751}

Simplify the expression

More Steps

Evaluate

\frac{1}{5751}

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

\frac{1}{5751}

Simplify the radical expression

\frac{1}{5751}

Simplify the radical expression

More Steps

Evaluate

5751

Write the expression as a product where the root of one of the factors can be evaluated

81 \times 71

Write the number in exponential form with the base of 9

9^{2} \times 71

The root of a product is equal to the product of the roots of each factor

9^{2} \times 71

Reduce the index of the radical and exponent with 2

971

\frac{1}{9 71}

Multiply by the Conjugate

\frac{71}{9 71 \times 71}

Multiply the numbers

More Steps

Evaluate

971 \times 71

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

9 \times 71

Multiply the terms

639

\frac{71}{639}

a = \pm \frac{71}{639}

Separate the equation into 2 possible cases

a = \frac{71}{639} a = - \frac{71}{639}

Solution

a_{1} = - \frac{71}{639}, a_{2} = \frac{71}{639}

Alternative Form

a_{1} \approx - 0.013186, a_{2} \approx 0.013186

Show Solution