Đáp án:
$A = \frac{\sqrt[]{15}+1}{2}$
$B = \frac{\sqrt{7}+1}{2}$
$C = \frac{\sqrt[]{15}-1}{2}$
Giải thích các bước giải:
A = $\sqrt[]{\frac{8+\sqrt[]{15}}{2}}$
⇒ $2A = \sqrt[]{16+2\sqrt[]{15}}$
⇔ $2A = \sqrt[]{15+2\sqrt[]{15}+1}$
⇔ $2A = \sqrt[]{(\sqrt[]{15} + 1)^{2}}$
⇔ $2A = \sqrt[]{15} + 1$
⇒ $A = \frac{\sqrt[]{15}+1}{2}$
B = $\sqrt[]{\frac{4+\sqrt[]{7}}{2}}$
⇒ $2B = \sqrt[]{8+2\sqrt[]{7}}$
⇔ $2B = \sqrt[]{7+2\sqrt[]{7}+1}$
⇔ $2B = \sqrt[]{(\sqrt[]{7}+1)^{2}}$
⇔ $2B = \sqrt[]{7} + 1$
⇒ $B = \frac{\sqrt{7}+1}{2}$
C = $\sqrt[]{\frac{8-\sqrt[]{15}}{2}}$
⇒ $2C = \sqrt[]{16-2\sqrt{15}}$
⇔ $2C = \sqrt[]{15-2\sqrt[]{15}+1}$
⇔ $2C = \sqrt[]{(\sqrt[]{15}-1)^{2}}$
⇔ $2C = \sqrt[]{15} - 1$
⇒ $C = \frac{\sqrt[]{15}-1}{2}$
