Question

W x and y are three integers w is 2 less than x y is 2 more than x prove that wy+ 4 =x^2

Answer 1

w + 2 = x

x + 2 = y

Cross multiply

y(w+2) = x(x+2)

wy + 2y = x^2 + 2x

make x the subject of the equation

x = y - 2

substitute this in place of (x) in 2x

wy + 2y = x^2 + 2(y-2)

wy + 2y = x^2 + 2y - 4

wy + 2y - 2y + 4 = x^2

wy + 4 = x^2

Answer 2

To solve this equation, let's generalize the question and prove it using basic algebraic methods.

So we are given that:
1. w is 2 less than x (w=x-2)
2. y is 2 more than x (y=x+2)

We are asked to prove that: wy + 4 = x^2

Let's substitute the values of w and y in terms of x into the equation

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

=> x^2 - 4 + 4 = x^2

This equation holds true for all integer values of x, as x^2 = x^2.

Thus, the given statement is proved.