Question

-3^x and -4^(2x), which one is greater when x is a positive odd number

Answer 1

Answer:

Step-by-step explanation:

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.