Question

若a+b=3,ab=1 求(a^3)b+ab^3和（a-b)^2

Answer 1

∵a+b=3,ab=1

∴(a+b)^2=9,即a^2+b^2+2ab=9

∴a^2+b^2=7

(a^3)b+ab^3=ab(a^2+b^2)=1×7=7

(a-b)^2=a^2+b^2-2ab=7-2×1=5