Question

plz help me with this question..

Answer 1

The value is -0.55

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Answer 2

Answer

$here \: given \\ x = \frac{ \sqrt{5} + 1}{3} \\ \: 3 {x}^{3} - 4 {x}^{2} + 2 \\ = {x}^{2}(3x - 4) + 2 \\ = ( { \frac{ \sqrt{5} + 1}{3} )}^{2} (3 \times \frac{ \sqrt{5} + 1}{3} - 4) + 2 \\ = \frac{ 5 + 2 \sqrt{5} + 1 }{9} ( \sqrt{5 } + 1 - 4) + 2 \\ = \frac{(5 + 2 \sqrt{5} + 1)( \sqrt{5} - 3)}{9} + 2 \\ = \frac{(6 + 2 \sqrt{5} )( \sqrt{5} - 3)}{9} + 2 \\ = \frac{6 \sqrt{5} - 18 + 10 - 6 \sqrt{5} }{9} + 2 \\ = \frac{ - 8}{9} + 2 \\ = \frac{ - 8 + 18}{9} \\ = \frac{10}{9}$

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