Question

Find 3 consecutive odd numbers where the product of the smaller two numbers is 46 less than the square of the largest number.@jiraya @alli14344

Answer 1

Let x be the smallest of the three numbers.

the numbers would be x, x+2, x+4 (understand why?)

so the product of the smallest two would be:
x(x+2)

46 less than the square of the largest would be:
(x+4)^2 - 46

set these equal and solve.

x(x+2) = (x+4)^2 - 46

Answer 2

5, 7, 9

Let X be the first odd number, so X+2 will be the next odd number, and X+4 will be the final odd number.

X * (X+2) = (X+4)2 - 46

X2+2X = X2+8X+16-46

X2+2X = X2+8X-30

Rearrange to get like terms to one side,

6X = 30

X =5

So the next two odd numbers would be 7 & 9

We can check the results:

5*7 =? 92 -46

35 =? 81-46

35 = 35 So the results are correct.