Question

If x is a whole number and 437 = (21 + x)(21 - x), then x =

Answer 1

2

Explanation:

In general,
`(a+b)(a-b)=a^2-b^2`.

So we have here that:

`437=21^2-x^2`

`437=441-x^2`

We went
`-x^2` by itself first.

Subtract 441 on both sides:

`437-441=-x^2`

`-4=-x^2`

Multiply both sides by -1:

`4=x^2`

Take the square root of boht sides:

`\pm √(4)=x`

`\pm 2=x`

So both 2 and -2 would satisfy the equation.

Only one of these is a whole number.

The whole numbers consist of the elements that you can count with and 0.

The whole number set is {0,1,2,3,4,5,6,7,...}

So 2 is the answer.

Check:

Replace x with 2:

437=(21+2)(21-2)

437=(23)(19)

437=437 is a true equation so 2 is definitely a solution.