((1)/(1+\sqrt(3))+(1)/(1-\sqrt(3)))((-14)/(\sqrt(7)))

asked by guest
on Nov 23, 2024 at 2:53 am



You asked:

Evaluate the expression: (11+3+11−3)⋅−147\left(\frac{1}{1 + \sqrt{3}} + \frac{1}{1 - \sqrt{3}}\right) \cdot \frac{-14}{\sqrt{7}}

MathBot Answer:

(11+3+11−3)⋅−147=−27⋅(11−3+11+3)≈5.29150262212918118100323150727852\left(\frac{1}{1 + \sqrt{3}} + \frac{1}{1 - \sqrt{3}}\right) \cdot \frac{-14}{\sqrt{7}} = - 2 \sqrt{7} \cdot \left(\frac{1}{1 - \sqrt{3}} + \frac{1}{1 + \sqrt{3}}\right) \approx 5.29150262212918118100323150727852

(11+3+11−3)⋅−147=(11+3+11−3)⋅−14⋅17=(11+3+11−3)⋅−2⋅7=−2⋅7⋅(11+3+11−3)\begin{aligned}\left(\frac{1}{1 + \sqrt{3}} + \frac{1}{1 - \sqrt{3}}\right) \cdot \frac{-14}{\sqrt{7}}&=\left(\frac{1}{1 + \sqrt{3}} + \frac{1}{1 - \sqrt{3}}\right) \cdot -14 \cdot \frac{1}{\sqrt{7}}\\&=\left(\frac{1}{1 + \sqrt{3}} + \frac{1}{1 - \sqrt{3}}\right) \cdot -2 \cdot \sqrt{7}\\&=-2 \cdot \sqrt{7} \cdot \left(\frac{1}{1 + \sqrt{3}} + \frac{1}{1 - \sqrt{3}}\right)\end{aligned}

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