Question

the product of two positive consecutive integers is equal to 56. find the two integers.

Answer 1

The answer is 7 & 8.

Answer 2

$Let \: the \:two\: positive\: consecutive\: integers\: be\: \frac{x}{y}\: and \:\frac{x}{y}+1\\ A/Q\\ \frac{x}{y}\times(\frac{x}{y}+1)=56\\=>\frac{{x}^{2}}{{y}^{2}}+\frac{x}{y}=56\\=>\frac{x}{y}+1=\frac{56y}{x}\\=>\frac{x}{y}=\frac{56y-x}{x}\\So\: the \: integers \: are\: \frac{56y-x}{x} \: and \frac{56y}{x}$

Now,
56y/x+56y-x/x=56
=>112y-x/x=56
=>112y-x=56x
=>112y=57x=>y=57x/112 Now,by putting the value of y we have,
56y/x=\frac{56x(57/112x)/x=3192/112 So the integers are 3080/112 and 3192/112