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Question 1
The sum of a proper fraction and its reciprocal is $$\frac{61}{30}$$. Find the fraction.
Solution
Let the fraction be $$x$$
According to ques,
=> $$x+\frac{1}{x}=\frac{61}{30}$$
=> $$\frac{x^2+1}{x}=\frac{61}{30}$$
=> $$30x^2-61x+30=0$$
=> $$30x^2-36x-25x+30=0$$
=> $$6x(5x-6)-5(5x-6)=0$$
=> $$(6x-5)(5x-6)=0$$
=> $$x=\frac{5}{6},\frac{6}{5}$$
=> Ans - (B)
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