a)\(A=^3\sqrt{20+14\sqrt{2}}+^3\sqrt{20-14\sqrt{2}}\)
=> \(A^3=\left(\sqrt[3]{20+14\sqrt{2}}+\sqrt[3]{20-14\sqrt{2}}\right)^3\)
\(=20+14\sqrt{2}+20-14\sqrt{2}\)
\(+3\left(\text{}^3\sqrt{20+14\sqrt{2}}+^3\sqrt{20-14\sqrt{2}}\right)\left(^3\sqrt{20+14\sqrt{2}}.^3\sqrt{20-14\sqrt{2}}\right)\)
\(=40+3A.^3\sqrt{\left(20+14\sqrt{2}\right)\left(20+14\sqrt{2}\right)}\)
\(\Rightarrow A^3=40+3.A.2\)
=> \(A^3-6A-40=0\)
<=> \(A^3-16A+10A-40=0\)
<=> \(A\left(A-4\right)\left(A+4\right)+10\left(A-4\right)=0\)
<=> \(\left(A-4\right)\left(A^2+4A+10\right)=0\)
<=> A = 4 ( vì \(A^2+4A+10=\left(A+2\right)^2+6>0\))
Vậy A = 4.
b/ \(B=^3\sqrt{26+15\sqrt{3}}-^3\sqrt{26-15\sqrt{3}}\)
=> \(B^3=\left(^3\sqrt{26+15\sqrt{3}}-^3\sqrt{26-15\sqrt{3}}\right)^3\)
\(=26+15\sqrt{3}-26+15\sqrt{3}\)
\(-3\left(^3\sqrt{26+15\sqrt{3}}-^3\sqrt{26-15\sqrt{3}}\right).^3\sqrt{26+15\sqrt{3}}.^3\sqrt{26-15\sqrt{3}}\)
\(=30\sqrt{3}-3B.1\)
=> \(B^3+3B-30\sqrt{3}=0\)
<=> \(B^3-12B+15B-30\sqrt{3}=0\)
<=> \(B\left(B-2\sqrt{3}\right)\left(B+2\sqrt{3}\right)+15\left(B-2\sqrt{3}\right)=0\)
<=> \(\left(B-2\sqrt{3}\right)\left(B^2+2\sqrt{3}B+15\right)=0\)
<=> \(B-2\sqrt{3}=0\)( vì \(B^2+2\sqrt{3}B+15=\left(B+\sqrt{3}\right)^2+12>0\))
<=> \(B=2\sqrt{3}\)
