Упр.17.15 ГДЗ Мерзляк Поляков 8 класс (Алгебра)

1) 49x^2-2; 5) a-4va+4;
2) 36p-64q,если p?0,q?0; 6) 5+v5;
3) c-100,если c?0; 7) v3p-p;
4) a-8bva+16b^2; 8) v12+v32.

1. $$49x^2-2=(7x)^2-(\sqrt2)^2=(7x-\sqrt2)(7x+\sqrt2).$$
2. $$36p-64q=4(9p-16q)=4\bigl((3\sqrt p)^2-(4\sqrt q)^2\bigr)=4(3\sqrt p-4\sqrt q)(3\sqrt p+4\sqrt q).$$
3. $$c-100=(\sqrt c)^2-10^2=(\sqrt c-10)(\sqrt c+10).$$
4. $$a-8b\sqrt a+16b^2=(\sqrt a)^2-2\sqrt a\cdot 4b+(4b)^2=(\sqrt a-4b)^2.$$
5. $$a-4\sqrt a+4=(\sqrt a)^2-2\sqrt a\cdot 2+2^2=(\sqrt a-2)^2.$$
6. $$5+\sqrt5=(\sqrt5)^2+\sqrt5=\sqrt5(\sqrt5+1).$$
7. $$\sqrt{3p}-p=\sqrt3\sqrt p-(\sqrt p)^2=\sqrt p(\sqrt3-\sqrt p).$$
8. $$\sqrt{12}+\sqrt{32}=\sqrt4\sqrt3+\sqrt4\sqrt8=\sqrt4(\sqrt3+\sqrt8)=2(\sqrt3+2\sqrt2).$$

Ответ

1) $$49x^2-2=(7x-\sqrt2)(7x+\sqrt2);$$
2) $$36p-64q=4(3\sqrt p-4\sqrt q)(3\sqrt p+4\sqrt q);$$
3) $$c-100=(\sqrt c-10)(\sqrt c+10);$$
4) $$a-8b\sqrt a+16b^2=(\sqrt a-4b)^2;$$
5) $$a-4\sqrt a+4=(\sqrt a-2)^2;$$
6) $$5+\sqrt5=\sqrt5(\sqrt5+1);$$
7) $$\sqrt{3p}-p=\sqrt p(\sqrt3-\sqrt p);$$
8) $$\sqrt{12}+\sqrt{32}=2(\sqrt3+2\sqrt2).$$