Đáp án:
Linh hoạt sử dụng các hằng đẳng thức sau:
`{((a+b)^3=a^3+3a^2b+3ab^2+b^3),((a-b)^3=a^3-3a^2b+3ab^2-b^3),((a+b)^2=a^2+2ab+b^2):}`
Giải thích các bước giải:
`a)x=((\sqrt{5}+2)\root{3}{17\sqrt{5}-38})/(\sqrt{5}+\sqrt{14-6\sqrt{5}})`
`x=((\sqrt{5}+2)\root{3}{5\sqrt{5}-3*5*2+3*4*\sqrt{5}-2^3})/(\sqrt{5}+\sqrt{9-2.3.\sqrt{5}+5})`
`x=((\sqrt{5}+2)\root{3}{(\sqrt{5}-2)^3})/(\sqrt{5}+\sqrt{(3-\sqrt{5})^2})`
`x=((\sqrt{5}+2)(\sqrt{5}-2))/(\sqrt{5}+3-\sqrt{5})`
`x=(5-4)/3=1/3`
`=>A=(3*1/27+8*1/9-2)^{2020}`
`=>A=(1/9+8/9-2)^{2020}`
`=>A=(-1)^{2020}=1`
`b)x=\root{3}{7+5\sqrt{2}}-1/(\root{3}{7+5\sqrt{2}})`
`x=\root{3}{2\sqrt{2}+3*2*1+3*\sqrt{2}*1+1^3}-1/(\root{3}{2\sqrt{2}+3*2*1+3*\sqrt{2}*1+1^3})`
`x=\root{3}{(\sqrt{2}+1)^3}-1/(\root{3}{(\sqrt{2}+1)^3})`
`x=\sqrt{2}+1-1/(\sqrt{2}+1)`
`x=\sqrt{2}+1-(\sqrt{2}-1)/(2-1)`
`x=\sqrt{2}+1-\sqrt{2}+1=2`
`=>B=(2^3+3.2-14)^{10}`
`=>B=(8+6-14)^{10}`
`=>B=0^{10}=0`
