Solve a^22005-1 - ScanMath

Question

Simplify the expression

2005 a^{2} - 1

Evaluate

a^{2} \times 2005 - 1

Solution

2005 a^{2} - 1

Show Solution

a_{1} = - \frac{2005}{2005}, a_{2} = \frac{2005}{2005}

Alternative Form

a_{1} \approx - 0.022333, a_{2} \approx 0.022333

Evaluate

a^{2} \times 2005 - 1

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

a^{2} \times 2005 - 1 = 0

Use the commutative property to reorder the terms

2005 a^{2} - 1 = 0

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

2005 a^{2} = 0 + 1

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

2005 a^{2} = 1

Divide both sides

\frac{2005 a ^{2}}{2005} = \frac{1}{2005}

Divide the numbers

a^{2} = \frac{1}{2005}

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

a = \pm \frac{1}{2005}

Simplify the expression

More Steps

Evaluate

\frac{1}{2005}

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

\frac{1}{2005}

Simplify the radical expression

\frac{1}{2005}

Multiply by the Conjugate

\frac{2005}{2005 \times 2005}

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

\frac{2005}{2005}

a = \pm \frac{2005}{2005}

Separate the equation into 2 possible cases

a = \frac{2005}{2005} a = - \frac{2005}{2005}

Solution

a_{1} = - \frac{2005}{2005}, a_{2} = \frac{2005}{2005}

Alternative Form

a_{1} \approx - 0.022333, a_{2} \approx 0.022333

Show Solution