Question

What is the missing constant term in the perfect square that starts with x²+6x?

Answer 1

The expression given to us is: x²+6x

Now, we know that the second term is twice the square root of the first and the last terms. Let us call the last term as $y^2$. Thus our given expression will become:

$x^2+6x+y^2$.

Now, since the middle term is 6x and since we know that the second term is twice the square root of the first and the last terms, therefore,

$6x=2\times \sqrt{x^2} \times \sqrt{y^2}$

$6x=2\times x\times y$

$\therefore y=3$ (By dividing both sides by 2x)

Therefore, the missing term is 3.

Answer 2

The missing term is 9