Question

The sum of the squares of two consecutive positive integers is $545$ , then the integers are $17$ and $19$.
If true then enter $1$ and if false then enter $0$

Answer 1

Let $x$ be one of the positive integers.

Then the other integer is $x+1$, $x\in z$
Since the sum of the squares of the integers is $545$, we get
$x^2+(x+1{)}^2=545$
$\Rightarrow 2x^2+2x-544=0$ or $x^2+x-272=0$
$\Rightarrow x^2+17x-16x-272=0$ or $x(x+17)-16(x+17)=0$
$\Rightarrow (x-16)(x+17)=0$
Here $x=16$ or $x=-17$

But $x$ is a positive integer.

Therefore reject $x=-17$ and take $x=16$
Hence, two consecutive positive integers are $16$ and $17$.

Then statement is false answer $0$.