If (image) , where x, y, z are integers, then find the values of x, y, z.
Answers
Answer with explanation is given in the figures. Refer them.
By an assumption the values of x, y and z are found!
First we have to make the given long fraction in the question (the RHS of tbe question) into a simple fraction.
For this, we have to start simplifying it from bottom.
Thus, at LHS (in the figure),
=> y + 1/z becomes (yz + 1)/z first.
=> 1/((yz + 1)/z) becomes z/(yz + 1).
=> On adding x, it becomes (xyz + x + z)/(yz + 1).
=> Now, 1/((xyz + x + z)/(yz + 1)) becomes (yz + 1)/(xyz + x + z), then (yz + 1)/(x(yz + 1) + z).
This time, at RHS, 37/13 will be deduced by 2 from LHS to become 11/13.
Hence we get (yz + 1)/(x(yz + 1) + z) = 11/13.
By taking the reciprocal of both sides, we get x + (z/(yz + 1)) = 1 + 2/11.
Here I expanded the denominator of 2/11, i.e., 11, as 2 × 5 + 1.
Thus, x + (z/(yz + 1)) = 1 + 2/(2 × 5 + 1)
From both sides, we get the following:
=> Fractions at both sides are added by an integer. Here it's x at LHS and 1 at RHS. Thus we can assume that x = 1.
=> From the denominator, we can see that the numerator is multiplied by another integer, then it is added by 1. From this, we can assume that z = 2.
=> As rest, we assume y = 5.
Hence found!!!
