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Question Number 170150 by daus last updated on 17/May/22

Answered by Rasheed.Sindhi last updated on 17/May/22

m^2 =n+2..........(i) n^2 =m+2...........(ii) 4mn−m^3 −n^3 =? (i)−(ii): m^2 −n^2 =−(m−n) (m−n)(m+n)=−(m−n) (m−n)(m+n)+(m−n)=0 (m−n)(m+n+1)=0 m=n^★ ∣ m+n=−1 (i)+(ii): m^2 +n^2 =m+n+4 (m+n)^2 −2mn=m+n+4 (−1)^2 −2mn=−1+4=3 mn=−1 4mn−(m^3 +n^3 ) =4mn−(m+n)^3 +3mn(m+n) =4(−1)−(−1)^3 +3(−1)(−1) =−4+1+3=0 ^★ m=n (i)⇒m^2 −m−2=0 m=n=((1±(√(1+8)))/2)=((1±3)/2)=2,−1 4mn−m^3 −n^3 =4m^2 −m^3 −m^3 =2m^2 (2−m) = { ((2(2)^2 (2−2)=0)),((2(−1)^2 (2+1)=6)) :}

m2=n+2..........(i)n2=m+2...........(ii)4mn−m3−n3=?(i)−(ii):m2−n2=−(m−n)(m−n)(m+n)=−(m−n)(m−n)(m+n)+(m−n)=0(m−n)(m+n+1)=0m=n★∣m+n=−1(i)+(ii):m2+n2=m+n+4(m+n)2−2mn=m+n+4(−1)2−2mn=−1+4=3mn=−14mn−(m3+n3)=4mn−(m+n)3+3mn(m+n)=4(−1)−(−1)3+3(−1)(−1)=−4+1+3=0★m=n(i)⇒m2−m−2=0m=n=1±1+82=1±32=2,−14mn−m3−n3=4m2−m3−m3=2m2(2−m)={2(2)2(2−2)=02(−1)2(2+1)=6

Commented by peter frank last updated on 19/May/22

thanks

thanks

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