The product of two consecutive even integers is 16 more then 8 times the smallest integer. Determine the integers.

Question

parthkohli · Answer

If x is the smaller, then x + 2 is the bigger one. Let's put up an equation here.

$\Large \color{MidnightBlue}{\Rightarrow x(x + 2) = 16 + 8x }$

$\Large \color{MidnightBlue}{\Rightarrow x^2 + 2x = 16 + 8x }$

$\Large \color{MidnightBlue}{\Rightarrow x^2 - 6x - 16 = 0 }$

Use the quadratic formula to solve.

parthkohli · Answer

@mr.awesome two consecutive EVEN. I think you misread that part.

anonymous · Answer

$$n(n+2)=n+16 $$

$$n^2+2n=n+16 $$

$$n^2+n=16 $$

$$n^2+n-16=0 $$

$$x=   \frac  {  -1\pm  \sqrt  { 65  }}{ 2}\\ x= \frac{      -1     +   \sqrt{    65   }} {   2 }\\  $$