\frac{\left(121-100\right)^2}{100}+\frac{\left(288-150\right)^2}{150}+\frac{\left(91-250\right)^2}{250}

asked by guest
on Jan 15, 2025 at 5:43 pm



You asked:

Evaluate the expression: \(\frac{{\left( 121 - 100 \right)}^{2}}{100} + \frac{{\left( 288 - 150 \right)}^{2}}{150} + \frac{{\left( 91 - 250 \right)}^{2}}{250}\)

MathBot Answer:

\[\frac{{\left( 121 - 100 \right)}^{2}}{100} + \frac{{\left( 288 - 150 \right)}^{2}}{150} + \frac{{\left( 91 - 250 \right)}^{2}}{250} = \frac{116247}{500} = 232.494\]

\[\begin{aligned}\frac{{\left( 121 - 100 \right)}^{2}}{100} + \frac{{\left( 288 - 150 \right)}^{2}}{150} + \frac{{\left( 91 - 250 \right)}^{2}}{250}& = \left(121 - 100\right)^{2} \cdot \frac{1}{100} + \left(288 - 150\right)^{2} \cdot \frac{1}{150} + \left(91 - 250\right)^{2} \cdot \frac{1}{250}\\& = 21^{2} \cdot \frac{1}{100} + \left(288 - 150\right)^{2} \cdot \frac{1}{150} + \left(91 - 250\right)^{2} \cdot \frac{1}{250}\\& = \frac{441}{100} + \left(288 - 150\right)^{2} \cdot \frac{1}{150} + \left(91 - 250\right)^{2} \cdot \frac{1}{250}\\& = \frac{441}{100} + 138^{2} \cdot \frac{1}{150} + \left(91 - 250\right)^{2} \cdot \frac{1}{250}\\& = \frac{441}{100} + \frac{19044}{150} + \left(91 - 250\right)^{2} \cdot \frac{1}{250}\\& = \frac{441}{100} + \frac{3174}{25} + \left(91 - 250\right)^{2} \cdot \frac{1}{250}\\& = \frac{441}{100} + \frac{3174}{25} + \left(-159\right)^{2} \cdot \frac{1}{250}\\& = \frac{441}{100} + \frac{3174}{25} + \frac{25281}{250}\\& = \frac{13137}{100} + \frac{25281}{250}\\& = \frac{116247}{500}\end{aligned}\]

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