Question

X, y, x and w are integers. the expression x - y - z is even and the expression y - z - w is odd. if x is even what must be true?

Answer 1

let x-y-z=even___(1)
y-z-w=odd._____(2)
(1)+(2)
x-w=even+odd
-w=even+odd-even
w=-even-odd+even.
w=odd number
is true..

Answer 2

Answer:

W is odd.This statement is must true.

Step-by-step explanation:

Givn that x is even.

Y-z should result be even and it's possible only if both y and z are of same even/odd nature

Case 1: Y is even and z is even then Y-Z = even and w must be odd to make Y-Z-W odd.

Case 2: Y is odd and Z is odd

Then Y-Z = even and W must be odd to make Y-Z-W odd.

In both the cases, W is odd ( It is must true).

It is a problem of Algebra.

Some formulas of Algebra,

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab − b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)³ − 3ab(a + b)

a³ - b³ = (a -b)³ + 3ab(a - b)

${a}^{2} - {b}^{2} = (a + b)(a - b)$

${a}^{2} + {b}^{2} = {(a + b)}^{2} - 2ab$

${a}^{2} + {b}^{2} = {(a - b)}^{2} + 2ab$