Question

Find 3 consecutive even numbers where the product of the smaller two numbers is 64 less than the square of the largest number. @johnweldon1993 @Jhannybean

Answer 1

hmm...well we only want even numbers...so lets let the first number be 2x...and we want consecutive even numbers...so we can do 2x + 2 and 2x + 4

Now...the product of the smaller 2 is 64 less than the square of the largest number

\[2x \times (2x + 2) = (2x + 4)^2 - 64\]

\[4x^2 + 4x = 4x^2 + 16x - 48\]

\[-12x = -48\]

\[x = 4\]

so if 'x' is equal to 4...we can go back to the original

2x , 2x + 2, 2x + 4 thing...we know x = 4 so

2(4), 2(4) + 2, 2(4) + 4

our numbers are

8, 10, 12

Answer 2

now we can check....product of 2 smaller

8 X 10 = 80

is 64 less than the square of the bigger

12² = 144

144 - 64 = 80

so they work