Solve 10001-2y^2 - ScanMath

Question

Find the roots

y_{1} = - \frac{20002}{2}, y_{2} = \frac{20002}{2}

Alternative Form

y_{1} \approx - 70.714214, y_{2} \approx 70.714214

Evaluate

10001 - 2 y^{2}

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

10001 - 2 y^{2} = 0

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

- 2 y^{2} = 0 - 10001

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

- 2 y^{2} = - 10001

Change the signs on both sides of the equation

2 y^{2} = 10001

Divide both sides

\frac{2 y ^{2}}{2} = \frac{10001}{2}

Divide the numbers

y^{2} = \frac{10001}{2}

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

y = \pm \frac{10001}{2}

Simplify the expression

More Steps

Evaluate

\frac{10001}{2}

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

\frac{10001}{2}

Multiply by the Conjugate

\frac{10001 \times 2}{2 \times 2}

Multiply the numbers

More Steps

Evaluate

10001 \times 2

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

10001 \times 2

Calculate the product

20002

\frac{20002}{2 \times 2}

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

\frac{20002}{2}

y = \pm \frac{20002}{2}

Separate the equation into 2 possible cases

y = \frac{20002}{2} y = - \frac{20002}{2}

Solution

y_{1} = - \frac{20002}{2}, y_{2} = \frac{20002}{2}

Alternative Form

y_{1} \approx - 70.714214, y_{2} \approx 70.714214

Show Solution