Question

A natural number when increased by 84 equals 160 times its reciprocal find the number by use factorization

Answer 1

Dear Student,

Let the natural number be x.

Then, according to question,
x+84=160/x
x2+84x=160
x2+84x-160=
0The above equation does not factorize, so there is not a natural number according to the given condition.
We can find the roots of the above equation using 
the quadratic formula −b±√b2−4ac√2a−84−7696√2 
and −84+7696√2
⇒ −84−7696√2 and −84+7696√2

Regards