Question

pozz help me with q44

Answer 1

$a = {3}^{ \frac{1}{4} } + {3}^{ \frac{ - 1}{4} } \\ {a}^{2} = {3}^{ \frac{1}{2} } + {3}^{ \frac{ - 1}{2} } + 2 \\ \\ b = {3}^{ \frac{1}{4} } - {3}^{ \frac{ - 1}{4} } \\ {b}^{2} = {3}^{ \frac{1}{2} } + {3}^{ \frac{ - 1}{2} } - 2 \\ {a}^{2} + {b}^{2} = 2 ({3}^{ \frac{1}{2} } ) + 2 ({3}^{ - \frac{1}{2} } ) \\ now \\ \\ { ({a}^{2} + {b}^{2}) }^{2} = 4( {3}^{} ) + 4( \frac{1}{3} ) + 8 \\ = \frac{36 + 4 + 8}{3} \\ = \frac{48}{3} = 16 \\ \\ so \\ 4( { {a}^{2} + {b}^{2} ) }^{2} = 4 \times 16 = 64$
hope it will help you!