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Question 182231: Q.(((The product of two consecutive even numbers is 12 more than the square of the smaller number. Form an equation and solve it to find the numbers))).
Answer by mastermath(14)   (Show Source):
You can put this solution on YOUR website! Let x and (x+2) be the two consecutive even numbers.
Their product is x(x+2).
The product of two consecutive odd numbers is 12 more than the square of the smaller number.
The smaller number is x.
so, the equation becomes
x(x+2)= x²+ 12
x² + 2x = x² + 12
We can subtract x² on both the sides.
2x=12
now divide with 2 on both the sides
x=6.
x+2=6+2=8.
So, the smaller odd number is 6.
And the larger odd number is 8.
Proof:
The product of two consecutive even numbers is 12 more than the square of the smaller number.
The product of the numbers is 6 and 8 is 48.
Square of the smaller number (here 6) is 36.
So, add 12 to 36
so, 12 + 36 = 48.
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