既知(x+my)(x+ny)=x2+2xy-8y2,m2n+mn2の値を求める.

既知(x+my)(x+ny)=x2+2xy-8y2,m2n+mn2の値を求める.

(x+my)(x+ny)=x2+2xy-8y22,0x2+nxy+mny2=x2+(m+n)xy+mny2=x2+2xy-8y2,0=m+n=0,mn=-8,0=m2n+mn2=mn(m+n)=-8×2=-16.