Question

\(\sqrt[3]{2+\sqrt{5}}+\sqrt[3]{2-\sqrt{5}}=1\)

Answer 1

=> A^3= 2+\(\sqrt{5}\)+2-\(\sqrt{5}+3.\sqrt[3]{\left(2-\sqrt{5}\right)\left(2+\sqrt{5}\right)}\).A

=> \(A^3=4+3.\sqrt[3]{-1}.A\)

=> \(A^3=4-3A\)

=>\(A^3+3A-4=0\)

=>\(\left(A^3-A^2\right)+\left(A^2-A\right)+\left(4A-4\right)=0\)

=> (A-1)\(\left(A^2+A+4\right)=0\)

mà \(A^2+A+4=\left(A+\dfrac{1}{2}\right)+\dfrac{15}{4}>0\)

=> A-1=0

=> A=1

Answer 2

xin lỗi mình nhầm một chút, chỗ kia là \(\left(A+\dfrac{1}{2}\right)^2+\dfrac{15}{4}\)

nha