Question

1/(3√8)-1/(√8-√7)+1/(√7-√6)-1/(√6-√5)+1/(√7-6)=5

Answer 1

Answer:

$1−8−71+7−61−6−51+5−21=5, proved.</p><p></p><p>Step-by-step explanation:</p><p>Show that, \dfrac{1}{3-\sqrt{8}}-\dfrac{1}{\sqrt{8}-\sqrt{7}}+\dfrac{1}{\sqrt{7}-\sqrt{6}}-\dfrac{1}{\sqrt{6}-\sqrt{5}}+\dfrac{1}{\sqrt{5}-2}=53−81−8−71+7−61−6−51+5−21=5</p><p>L.H.S.=\dfrac{1}{3-\sqrt{8}}-\dfrac{1}{\sqrt{8}-\sqrt{7}}+\dfrac{1}{\sqrt{7}-\sqrt{6}}-\dfrac{1}{\sqrt{6}-\sqrt{5}}+\dfrac{1}{\sqrt{5}-2}=3−81−8−71+7−61−6−51+5−21</p><p>Rationalising numerator and denominator, we get</p><p>=\dfrac{1}{3-\sqrt{8}}\times \dfrac{3+\sqrt{8}}{3+\sqrt{8}}-\dfrac{1}{\sqrt{8}-\sqrt{7}}\times\dfrac{\sqrt{8}+\sqrt{7}}{\sqrt{8}+\sqrt{7}}+\dfrac{1}{\sqrt{7}-\sqrt{6}}\times \dfrac{\sqrt{7}+\sqrt{6}}{\sqrt{7}+\sqrt{6}}-\dfrac{1}{\sqrt{6}-\sqrt{5}}\times \dfrac{\sqrt{6}+\sqrt{5}}{\sqrt{6}+\sqrt{5}}+\dfrac{1}{\sqrt{5}-2}\times \dfrac{\sqrt{5}+2}{\sqrt{5}+2}=3−81×3+83+8−8−71×8+78+7+7−61×7+67</p><p>$

Answer 2

Answer:

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