Question

the product of two consecutive even numbers is 12 more than the square of the smaller number​

Answer 1

$\underline\mathfrak{ANSWER:-}$

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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)= x�+ 12

➟x� + 2x = x� + 12

➟We can subtract x� on both the sides.

➟2x=12now 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

∴12 + 36 = 48.

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