x^2-5x-24成為完全平方數(shù),x^2-5x-24>=0
(1)x^2-5x-24=0,解得x=8 或 x=-3
(2)x^2-5x-24>0
x^2-5x-24=(x-8)(x+3)
令(x+3)=n^2,(x-8)=m^2,
相減n^2-m^2=11,即(n-m)(n+m)=11
當(dāng)(n-m)=1,(n+m)=11,解得n=6,m=5,對(duì)應(yīng)x=33
(n-m)=11,(n+m)=1,解得n=6,m=-5,對(duì)應(yīng)x=33
(n-m)=-1,(n+m)=-11,解得n=-6,m=-5,對(duì)應(yīng)x=33
(n-m)=-11,(n+m)=-1,解得n=-6,m=5,對(duì)應(yīng)x=33
令(x+3)=-n^2,(x-8)=-m^2
相減m^2-n^2=11,即(m+n)(m-n)=11
當(dāng)(m+n)=1,(m-n)=11,解得m=6,n=-5,對(duì)應(yīng)x=-28
(m+n)=11,(m-n)=1,解得m=6,n=5,對(duì)應(yīng)x=-28
(m+n)=-1,(m-n)=-11,解得m=-6,n=5,對(duì)應(yīng)x=-28
(m+n)=-11,(m-n)=-1,解得m=-6,n=-5,對(duì)應(yīng)x=-28
總上x(chóng)=8,-3,33,-28