已知{m}^{2}+{n}^{2}=10,mn=3,求(m+n{)}^{2},(m-n{)}^{2}的值
问题描述:
已知{m}^{2}+{n}^{2}=10,mn=3,求(m+n{)}^{2},(m-n{)}^{2}的值
已知m^2+n^2=10,mn=3,求(m+n)^2,(m-n)^2的值
答
已知m^2+n^2=10,mn=3,2mn=6,-2mn=-6.
∴m^2+n^2+2mn=10+6=16,(m+n)²=16
m^2+n^2-2mn=10-6=4,(m-n)²=4.