Question

find the answer , please give correct ans and step

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Answer 1

$\tt\blue{\underline{Answer:}}$

$\green{\tt\therefore New \: eqn \to9 {x}^{2} - 28x + 3 = 0}$

$\tt \green{ \underline{Given :}} \\ \tt: \implies Eqn \to {3x}^{2} - 4x + 1 = 0 \\ \\ \tt: \implies Roots \: of \: eqn = \alpha \: and \: \beta \\ \\ \tt \red{ \underline{To \: Find:}} \\ \tt: \implies Eqn \: whose \: roots \: are \: \frac{ { \alpha }^{2} }{ \beta } \: and \: \frac{ { \beta }^{2} }{ \alpha }$

$\tt\orange{\underline{Step-by-step\:\:explanation:}}$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies {3x}^{2} - 4x + 1 = 0 \\ \\ \tt: \implies {3x}^{2} - 3x - x + 1 = 0 \\ \\ \tt: \implies 3x(x - 1) - 1(x - 1) = 0 \\ \\ \tt: \implies (3x - 1)(x - 1) = 0 \\ \\ \tt: \implies x = \frac{1}{3} \: and \: 1 \\ \\ \sf\therefore \alpha = \frac{1}{3} \: and \: \beta = 1 \\ \\ \bold{For \: new \: roots} \\ \tt: \implies Sum \: of \: roots = \frac{ { \alpha }^{2} }{ \beta } + \frac{ { \beta }^{2} }{ \alpha } \\ \\ \tt: \implies Sum \: of \: roots = \frac{ { \alpha }^{3} + { \beta }^{3} }{ \alpha \beta } \\ \\ \tt: \implies Sum \: of \: roots = \frac{ \bigg(\frac{1}{3} \bigg) ^{3} + {1}^{3} }{ \frac{1}{3} \times 1 } \\ \\ \tt: \implies Sum \: of \: roots = \frac{ \frac{1}{27} + 1 }{ \frac{1}{3} } \\ \\ \tt: \implies Sum \: of \: roots = \frac{1 + 27}{27} \times 3 \\ \\ \tt: \implies Sum \: of \: roots = \frac{28}{9} \\ \\ \bold{Again :} \\ \tt: \implies Product \: of \: roots = \frac{ { \alpha }^{2} }{ \beta } \times \frac{ { \beta }^{2} }{ \alpha } \\ \\ \tt: \implies Product \: of \: roots = \alpha \beta \\ \\ \tt: \implies Product \: of \: roots = \frac{1}{3} \times 1 \\ \\ \tt: \implies Product \: of \: roots = \frac{1}{3} \\ \\ \bold{For \: new \: eqn } \\ \tt: \implies New \: eqn \to {x}^{2} - (Sum \: of \: roots)x + (Product \: of \: roots) = 0 \\ \\ \tt: \implies New \: eqn \to {x}^{2} - \frac{28}{9}x + \frac{1}{3} = 0 \\ \\ \green{\tt: \implies New \: eqn \to9 {x}^{2} - 28x + 3 = 0}$

Answer 2

New equation = 9

hope it helps. pls thank