Question Number 102418 by Akeyz last updated on 09/Jul/20

Answered by Rasheed.Sindhi last updated on 09/Jul/20

^(★1:) x,y∈W(={0,1,2,3,...}) 2^x +3^y ∈E⇒2^x ,3^y ∈E ∨ 2^x ,3^y ∈O 3^y ∈O⇒2^x ∈O⇒x=0 2^x +3^y =72⇒2^0 +3^y =72 ⇒3^y =71⇒y∉W ∴The system has no solution in W ^(★2:) When only one of x , y is negative whole number. x∈Z^− ⇒ 0<2^x <1(or y∈Z^− ⇒ 0<2^y <1) ⇒3^y <2^x +3^y <3^y +1 ⇒ 2^x +3^y ∉W (Similar case when y∈Z^− ) ^(★3) When both x & y are negative whole numbers 0<2^x <1 ∧ 0<3^y <1 ⇒ 0<2^x +3^y <2 ∴ 2^x +3^y =72 is impossible This proves that the given system has no solution in Z ......... .....