Question

the sum of the reciprocals of two consecutive odd natural numbers is 12/35.find those number?

Answer 1

$\huge\boxed{\huge\boxed{ ANSWER: \ \bold{5}\ AND \ \bold{7} \ }}$

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Let the consecutive odd natural numbers be x and x + 2.

$\bold{\frac{1}{x}+\frac{1}{x+2}=\frac{12}{35}} \\ \\ \\ \bold{\frac{x+x+2}{x(x+2)}=\frac{12}{35}} \\ \\ \\ \bold{\frac{2x+2}{x(x+2)}=\frac{12}{35}} \\ \\ \\ \bold{2\times\frac{x+1}{x(x+2)}=2 \times \frac{6}{35}} \\ \\ \\ \bold{\frac{x+1}{x(x+2)}=\frac{6}{35}}$

$\bold{35(x+1)=6x(x+2)} \\ \\ \bold{35x+35=6x^2+12x} \\ \\ \bold{6x^2+12x-35x-35=0} \\ \\ \bold{6x^2-23x-35=0} \\ \\ \bold{6x^2-30x+7x-35=0} \\ \\ \bold{6x(x-5)+7(x-5)=0} \\ \\ \bold{(6x+7)(x-5)=0} \\ \\ \\ \bold{\therefore\ x=-\frac{7}{6} \ \ \ \ \ ; \ \ \ \ \ x=5}$

- 7/6 is not a natural number. So it can't be taken.

$\bold{\therefore\ x=\bold{5}} \\ \\ \\ \bold{x+2=\bold{7}}$

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$\huge\boxed{\huge\boxed{\huge\boxed{\bold{ \ THANK\ YOU.\ :-) \ }}}}$