Question

Помогите пожалуйста в д/з.)

Answer 1

$1)\ \ 7m=1\ ,\ n=3\\\\\underbrace {49m^2-14mn+n^2}_{(7m)^2-2\cdot 7m\cdot n+n^2}-\underbrace{21m+3n}=(7m-n)^2-3(7m-n)=\\\\\\=(7m-n)(7m-n-3)=(1-3)(1-3-3)=-2\cdot (-8)=16$

$2)\ \ m-n=3\ ,\ mn=5\\\\m^2+n^2=(m^2+n^2-2mn)+2mn=(m-n)^2+2mn=3^2+2\cdot 5=19\\\\\\3)\ \ m^2+n^2=7\ ,\ \ mn=6\\\\m^4+m^2n^2+n^2=(m^4+2m^2n^2+n^4)-m^2n^2=(m^2+n^2)^2-(mn)^2=\\\\=7^2-6^2=49-36=13$