Question

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

Answer 1

Answer:

2

Step-by-step 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:

$\pm \sqrt{4}=x$

$\pm 2=x$

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.