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Find rational numbers a and b so that (7+?5)/(7-?5)-(7-?5)/(7+?5)=a+(7?5/11)b

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a+frac7sqrt511b=frac7+sqrt57-sqrt5-frac7-sqrt57+sqrt5=frac49+5+14sqrt5-49-5+14sqrt549-5
Rightarrow frac28sqrt544=frac7sqrt511
a+frac7sqrt511b=0+frac7sqrt511(1)
Rightarrow a=0,b=1

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Deependra Verma

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