Question

Выделите квадрат двучлена
х²-8х-1
4х²-20х+25

Answer 1

$(apm b)^2=a^2pm 2ab+b^2quad Rightarrow quad a^2pm 2ab=(apm b)^2-b^2\\iliqquad x^2pm px=(xpm frac{p}{2})^2-(frac{p}{2})^2\\\underbrace {x^2-8x}-1=underbrace {(x-4)^2-4^2}_{x^2-8x}-1=(x-4)^2-16-1=(x-4)^2-17\\\4x^2-20x+25=4cdot Big (underbrace {x^2-5x}+frac{25}{4}Big )=4cdot Big (underbrace {(x-frac{5}{2})^2-(frac{5}{2})^2}_{x^2-5x}+frac{25}{4}Big )=\\=4cdot Big ((x-2,5)^2-frac{25}{4}+frac{25}{4}Big )=4cdot (x-2,5 )^2\\iliqquad 4x^2-20x+25=(2x-5)^2$