Algebra Question #14: Absolutely

Algebra Level 3

If A is a natural numbers and ∣ x ∣ + ∣ y ∣ = A |x| + |y| = A ∣ x ∣ − ∣ y ∣ = A + 2 |x| - |y| = A+2 Find y

Algebra Question

{-1,1} 1 -1 no solution

Paul Ryan Longhas by Paul Ryan Longhas , 24, Philippines

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1 solution

a b s ( x ) + a b s ( y ) = A . . . . ( 1 ) abs(x)+abs(y) = A ....(1) a b s ( x ) − a b s ( y ) = A + 2.... ( 2 ) abs(x)-abs(y) = A+2....(2) = > a b s ( y ) = − 1 =>abs(y) = -1 But, a b s ( y ) = [ 0 , + i n f i n i t y ) abs(y) =[0,+infinity) so, y has no solution.

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