Вычислить [tex]\sqrt{15+2\sqrt{26}}*\sqrt{4+\sqrt{1+2\sqrt{26}}}*\sqrt{4-\sqrt{1+2\sqrt{26}}}[/tex] Объясните пожалуйста. Created by XasiM. algebra-ru

tex] Объясните пожалуйста...

Artem112

Verified answer

$\sqrt{15+2\sqrt{26}}\sqrt{4+\sqrt{1+2\sqrt{26}}}\sqrt{4-\sqrt{1+2\sqrt{26}}}= \\\ =\sqrt{15+2\sqrt{26}}\sqrt{(4+\sqrt{1+2\sqrt{26}})(4-\sqrt{1+2\sqrt{26}})}= \\\ =\sqrt{15+2\sqrt{26}}\sqrt{16-1-2\sqrt{26}}= \\\ =\sqrt{15+2\sqrt{26}}\sqrt{15-2\sqrt{26}}= \\\ =\sqrt{(15+2\sqrt{26})(15-2\sqrt{26})}= \\\ =\sqrt{225-4\cdot26}=\sqrt{225-104}=\sqrt{121}=11$

2 votes Thanks 1

Alexаndr

Verified answer

$\sqrt{15+2\sqrt{26}}*\sqrt{4+\sqrt{1+2\sqrt{26}}}*\sqrt{4-\sqrt{1+2\sqrt{26}}}$
Последние два множителя можно подвести под общий корень(получим формулу вида a^2-b^2):
$\sqrt{15+2\sqrt{26}}*\sqrt{(4+\sqrt{1+2\sqrt{26}})*(4-\sqrt{1+2\sqrt{26}})}=\\=\sqrt{15+2\sqrt{26}}*\sqrt{15-2\sqrt{26}}$
И опять формула:
$\sqrt{(15+2\sqrt{26})*(15-2\sqrt{26})}=\sqrt{225-104}=\sqrt{121}=11$

1 votes Thanks 1

Answers & Comments

Verified answer

Verified answer

tex]...

tex]...

1 dva predmeta v summe stoyat 60000 rub esli stoimost pervogo umenshit na 20

1 najdite induktivnost dannoj katushki esli energiya magnitnogo polya sozdavae

1 vpisannaya v pryamougolnyj treugolnik okruzhnost v tochke kasaniya delit gipote

kub s rebrom 6 razbit na dve chasti ploskostyu prohodyashej cherez ego vershiny a v

4sm najdite sinus ostrogo ugla rombapozhalujsta po podrobnee i s formulami

tochka a0u0 ravnoudalena ot tochek b123 i s 134 najdite u i pozhalujs

najdite ploshad treugolnika postroennogo na vektorah a12 i b3 5 esli mozh

pomogite s resheniem zadach1 najti ugol mezhdu vektorami a2 koren2 i b 4 k

рекомендуемые вопросы

Helpful Links

Helpful Social