若x+y=5,xy=-11,则(x-y)2=?,x3+y3=?

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若x+y=5,xy=-11,则(x-y)2=?,x3+y3=?若x+y=5,xy=-11,则(x-y)2=?,x3+y3=?若x+y=5,xy=-11,则(x-y)2=?,x3+y3=?(x-y)^2

若x+y=5,xy=-11,则(x-y)2=?,x3+y3=?
若x+y=5,xy=-11,则(x-y)2=?,x3+y3=?

若x+y=5,xy=-11,则(x-y)2=?,x3+y3=?
(x-y)^2
=x^2+y^2-2xy
=(x^2+y^2+2xy)-4xy
=(x+y)^2-4xy
=5^2-4*(-11)
=25+44
=69
x^3+y^3
=(x+y)(x^2+y^2-xy)
=(x+y)[(x+y)^2-3xy]
=5*[5^2-3*(-11)]
=5*58
=290

(x-y)²=(x+y)²-4xy=25+4×11=69.
x³+y³=(x+y)(x²+y²-xy)=(x+y)[(x-y)²+xy]=5×(69-11)=290.

(x-y)2=(x+y)²-4xy=25+44=69
x3+y3=(x+y)(x²-xy+y²)=(x+y)[(x+y)²-3xy]=5(25+33)=290

(x-y)2=25+44=69
x3+y3=290

(x-y)2=(x+y)2-4xy= 25+44=69,(x+y)3=x3+y3+3xy(x+y) 可得x3+y3=(x+y)3-3xy(x+y)=270

x+y=5,xy=-11,
则 (x-y)^2=x^2+y^2-2xy
=(x^2+y^2+2xy)-4xy
=(x+y)^2-4xy=5^2-4*(-11)=25+44=69
x^3+y^3
=(x+y)(x^2+y^2-xy)=(x+y)[(x+y)^2-3xy]
=5*[5^2-3*(-11)]=5*58=290