1) 49 + 20√6 = 5² + 2*5*2√6 + (2√6)² = (5+2√6)²
2)
![\sqrt[6]{(5+2 \sqrt{6})^2} = \sqrt[3]{5+2 \sqrt{6}}](https://tex.z-dn.net/?f=%20%5Csqrt%5B6%5D%7B%285%2B2%20%5Csqrt%7B6%7D%29%5E2%7D%20%3D%20%5Csqrt%5B3%5D%7B5%2B2%20%5Csqrt%7B6%7D%7D%20)
3)
![\sqrt[3]{2 \sqrt{6}-5} * \sqrt[3]{2 \sqrt{6}+5}= \sqrt[3]{(2 \sqrt{6})^2 - 5^{2} } = \sqrt[3]{24 - 25} = \sqrt[3]{-1} =-1](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B2%20%5Csqrt%7B6%7D-5%7D%20%2A%20%5Csqrt%5B3%5D%7B2%20%5Csqrt%7B6%7D%2B5%7D%3D%20%5Csqrt%5B3%5D%7B%282%20%5Csqrt%7B6%7D%29%5E2%20%20-%20%205%5E%7B2%7D%20%20%7D%20%3D%20%5Csqrt%5B3%5D%7B24%20-%2025%7D%20%3D%20%5Csqrt%5B3%5D%7B-1%7D%20%3D-1)
1)0,027а¹²+b^9=(0,3а⁴)³+(b³)³=(0,3a⁴+b³)(0,09a⁸-0,3a⁴b³+b⁶)
2)20z²+3xy-15xz-4yz=(20z²-15xz)-(4yz-3xz)=5z(4z-3x)-y(4z-3x)=(4z-3x)(5z-y)
3)
(x-(2xy-3x))-4xy+5x-(7-(2-(4-xy-x-y))-25)=
x-2xy+3x-4xy+5x-(7-(2-4+xy+x+y)-25)=
x-2xy+3x-4xy+5x-(7-2+4-xy-x-y-25)=
x-2xy+3x-4xy+5x-7+2-4+xy+x+y+25=
x-2xy+3x-4xy+5x+xy+x+y+16=
10x-5xy+y+16=
10*2-5*2*5+5+16=
20-50+5+16=
-9
Х кв(х-2)-9(х-2)=0
(х-2)(х кв-9)=0