Упр.18.33 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) a^4+17a^2+16; 3) 2x^2-6xy+9y^2-6x+9;
2) 10x^2+2xy+y^2; 4) x^2+y^2-10x+14y+74.

1. $$a^4+17a^2+16=a^4+8a^2+16+9a^2=(a^2+4)^2+(3a)^2.$$
2. $$10x^2+2xy+y^2=9x^2+x^2+2xy+y^2=(3x)^2+(x+y)^2.$$
3. $$2x^2-6xy+9y^2-6x+9=(x^2-6xy+9y^2)+(x^2-6x+9)=(x-3y)^2+(x-3)^2.$$
4. $$x^2+y^2-10x+14y+74=(x^2-10x+25)+(y^2+14y+49)=(x-5)^2+(y+7)^2.$$

Ответ

1. $$a^4+17a^2+16=(a^2+4)^2+(3a)^2$$
2. $$10x^2+2xy+y^2=(3x)^2+(x+y)^2$$
3. $$2x^2-6xy+9y^2-6x+9=(x-3y)^2+(x-3)^2$$
4. $$x^2+y^2-10x+14y+74=(x-5)^2+(y+7)^2$$