Question

Prove that :
1/3+√7+1/√7+√5+1/√5+√3+1/√3+1=1

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

$\bf \frac{1}{3 + \sqrt{7} } + \frac{1}{ \sqrt{7} + \sqrt{5} } + \frac{1}{ \sqrt{5} + \sqrt{3} } + \frac{1}{ \sqrt{3} + 1} = 1 \\ \\ \tt \large \: RATIONALISING \: \: THE \: \: ABOVE \\ \\ \bf \frac{3 - \sqrt{7} }{9 - 7 } + \frac{ \sqrt{7} - \sqrt{5} }{ 7 - 5 } + \frac{ \sqrt{5} - \sqrt{3} }{5 - 3 } + \frac{ \sqrt{3} - 1}{ 3 - 1} = 1 \\ \\ \bf \frac{3 - \cancel{\sqrt{7} + \sqrt{7} - \sqrt{5} + \sqrt{5} - \sqrt{3} + \sqrt{3} }- 1}{ 2} = 1 \\ \\ \huge \bf \fcolorbox{red}{grey}{1 = 1}$