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The integeral values of x for which x2 + 7x +13 is perfect square are _____ &_____

The integeral values of x for which x2 + 7x +13 is perfect square are _____ &_____

Grade:12th Pass

1 Answers

Arun
25758 Points
2 years ago
Let $f(x)=x^2+7x+13$
$x^2+7x+13 $ is right between $(x+3)^2, x^2+6x+9$ and $(x+4)^2,x^2+8x+16$ for any integral value of $x.$
Now, subtract $f(x)$ from the nearest square higher than $f(x)$ , it will be equal to $0 $ .(*Remember we're finding perfect squares.)*
Here, $(x+4)^2- f(x)=0$
$\implies x+3=0 \implies x=-3$
Now, subtract the nearest square lower than $f(x)$ from $f(x)$ , it will be too , equal to zero.
Here , $f(x)-(x+3)^2=0$
$\implies x+4=0 \implies x=-4$
So the two values of $x$ are $\boxed {-3,-4}.$
 

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