(100-x^2)^1/2 / (100-x^2)^-1/2

asked by guest
on Nov 14, 2024 at 2:38 pm



You asked:

Evaluate the expression: \(\frac{\frac{\frac{{\left( 100 - {x}^{2} \right)}^{1}}{2}}{{\left( 100 - {x}^{2} \right)}^{-1}}}{2}\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{\frac{\frac{{\left( 100 - {x}^{2} \right)}^{1}}{2}}{{\left( 100 - {x}^{2} \right)}^{-1}}}{2} = \frac{\left(100 - x^{2}\right)^{2}}{4} \)

Expanded

\[\frac{\frac{\frac{{\left( 100 - {x}^{2} \right)}^{1}}{2}}{{\left( 100 - {x}^{2} \right)}^{-1}}}{2} = \frac{x^{4}}{4} - 50 x^{2} + 2500\]

Factored

\[\frac{\frac{\frac{{\left( 100 - {x}^{2} \right)}^{1}}{2}}{{\left( 100 - {x}^{2} \right)}^{-1}}}{2} = \frac{\left(x - 10\right)^{2} \left(x + 10\right)^{2}}{4}\]

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