Question

x+y+xy =80 find x.



please do it fast

Answer 1

Answer:

The only natural value of x is 26.

Explanation:

Since it is given that x , y are natural numbers such that $x>y$.

Also, $x+y+xy=80$

Subtract y from both the sides, we get

$x+y+xy-y=80-y$

Simplify we get,

$x+xy=80-y$

⇒ $x(1+y)=80-y$ or

$x=\frac{80-y}{1+y}$

Since, it is given  that $x>y$

⇒ $\frac{80-y}{1+y}>y$ or

$(80-y)>y(1+y)$

On simplifying we get,

$80-y> y+y^2$ or

$-y^2-2y+80>0$ or

$y^2+2y-80<0$

Now solving above quadratic equations we get,

$(y+10)(y-8)<0$

Since, y is a natural number, the only condition, we have $y<8$

The only possible values for $y={1, 2, 3,4 ,5,6,7}$.

Now, putting these y values in $x=\frac{80-y}{1+y}$, to find the natural value of x;

the result x=26 is an natural number only for y=3.