Question

Seja $x=$ $x= \sqrt{ \sqrt[3]{ \sqrt{ 54^{24} } } }$ e $y = 2 . \sqrt[3]{ \sqrt{ \sqrt[4]{ \sqrt{ \frac{1}{2}^{48} } } } }$
calcule $2x + 3y$

Answer 1

Temos que:

$x = \sqrt{ \sqrt[3]{ \sqrt{54^{24}} } } = \sqrt{ \sqrt[3]{54^{12}} } = \sqrt{54^4} = 54^2 = 2916$

 $y = 2* \sqrt[3]{ \sqrt{ \sqrt[4]{ \sqrt{ \frac{1}{2}^{48} } } } } = 2*\sqrt[3]{ \sqrt{ \sqrt[4]{ \frac{1}{2}^{24} } } } = 2*\sqrt[3]{ \sqrt{ \frac{1}{2}^6 } } = 2*\sqrt[3]{ \frac{1}{2}^3 } = 1$

Logo:

$2x + 3y = 2*(2916) + 3*(1) = 5832+3 = 5835$