Solve- - 313 - 1517- - 313 - 1715-

313+1517× 313+1715 ⇒ 313 4517×13+1715 ⇒ 3×17×15 45×15+17×17×1317×13×15 ⇒3757 765 6753315 ⇒0.702 ...

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Byju's Answer

Standard XII

Mathematics

Complex Numbers

Solve, - 31...

Question

Solve, $\frac{- 3}{13} + \frac{15}{17} \times \frac{- 3}{13} + \frac{17}{15}$ .

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Solution

$- \frac{3}{13} + \frac{15}{17} \times \frac{- 3}{13} + \frac{17}{15} \Rightarrow - \frac{3}{13} - \frac{45}{17 \times 13} + \frac{17}{15} \Rightarrow - 3 \times 17 \times 15 - 45 \times 15 + 17 \times 17 \times 13 17 \times 13 \times 15 \Rightarrow \frac{3757 - 765 - 675}{3315} \Rightarrow 0.702$

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Prove that:
(i) $\frac{1}{3 + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{3}} + \frac{1}{\sqrt{3} + 1} = 1$
(ii) $\frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \frac{1}{\sqrt{4} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{6}} + \frac{1}{\sqrt{6} + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{8}} + \frac{1}{\sqrt{8} + \sqrt{9}} = 2$