((8\sqrt(7)-7)+(9\sqrt(7)-9))/(2)*(\sqrt(7)+2)

asked by guest
on Sep 19, 2024 at 9:48 am



You asked:

Evaluate the expression: \(\frac{8 \cdot \sqrt{7} - 7 + 9 \cdot \sqrt{7} - 9}{2} \cdot \left(\sqrt{7} + 2\right)\)

MathBot Answer:

\[\frac{8 \cdot \sqrt{7} - 7 + 9 \cdot \sqrt{7} - 9}{2} \cdot \left(\sqrt{7} + 2\right) = \frac{\left(-16 + 17 \sqrt{7}\right) \left(2 + \sqrt{7}\right)}{2} \approx 67.31176179958131531451454178275334\]

\[\begin{aligned}\frac{8 \cdot \sqrt{7} - 7 + 9 \cdot \sqrt{7} - 9}{2} \cdot \left(\sqrt{7} + 2\right)& = \left(8 \cdot \sqrt{7} - 7 + 9 \cdot \sqrt{7} - 9\right) \cdot \frac{1}{2} \cdot \left(\sqrt{7} + 2\right)\\& = \left(\left(-7 + 8 \cdot \sqrt{7}\right) + 9 \cdot \sqrt{7} - 9\right) \cdot \frac{1}{2} \cdot \left(\sqrt{7} + 2\right)\\& = \left(\left(-7 + 17 \cdot \sqrt{7}\right) - 9\right) \cdot \frac{1}{2} \cdot \left(\sqrt{7} + 2\right)\\& = \left(-16 + 17 \cdot \sqrt{7}\right) \cdot \frac{1}{2} \cdot \left(\sqrt{7} + 2\right)\\& = \left(-16 + 17 \cdot \sqrt{7}\right) \cdot \frac{1}{2} \cdot \left(2 + \sqrt{7}\right)\\& = \left(-8 + \frac{17}{2} \cdot \sqrt{7}\right) \cdot \left(2 + \sqrt{7}\right)\end{aligned}\]

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