if x = 31/3 + 3 -1/3, thenwhatis the value of 3x3 - 9x rn a) 12 b) - Maths - Factorisation

Question

if x = 31/3 + 3 -1/3, then whatis the
value of 3x3 - 9x ?
rn
a) 12 b) 9 c)15 d) 10 how??

Gursheen kaur. · Accepted Answer

$x = 3^{\frac{1}{3}} + 3^{\frac{- 1}{3}} N o w, x^{3} = {(3^{\frac{1}{3}} + 3^{\frac{- 1}{3}})}^{3}$

$x^{3} = {(3^{\frac{1}{3}})}^{3} + {(3^{\frac{- 1}{3}})}^{3} + 3 {(3^{\frac{1}{3}})}^{2} (3^{\frac{- 1}{3}}) + 3 {(3^{\frac{- 1}{3}})}^{2} (3^{\frac{1}{3}}) \Rightarrow x^{3} = 3 + 3^{- 1} + 3 (3^{\frac{2}{3}}) (3^{\frac{- 1}{3}}) + 3 (3^{\frac{- 2}{3}}) (3^{\frac{1}{3}}) \Rightarrow x^{3} = 3 + \frac{1}{3} + 3^{1 + \frac{2}{3} - \frac{1}{3}} + 3^{1 - \frac{2}{3} + \frac{1}{3}} \Rightarrow x^{3} = 3 + \frac{1}{3} + 3^{\frac{4}{3}} + 3^{\frac{2}{3}} T h e v a l u e o f 3 x^{3} - 9 x = 3 (3 + \frac{1}{3} + 3^{\frac{4}{3}} + 3^{\frac{2}{3}}) - 9 (3^{\frac{1}{3}} + 3^{\frac{- 1}{3}}) = 9 + \frac{3}{3} + 3 \times 3^{\frac{4}{3}} + 3 \times 3^{\frac{2}{3}} - 9 \times 3^{\frac{1}{3}} - 9 \times 3^{\frac{- 1}{3}} = 9 + 1 + 3^{1 + \frac{4}{3}} + 3^{1 + \frac{2}{3}} - 3^{2} \times 3^{\frac{1}{3}} - 3^{2} \times 3^{\frac{- 1}{3}} = 9 + 1 + 3^{\frac{7}{3}} + 3^{\frac{5}{3}} - 3^{2 + \frac{1}{3}} - 3^{2 - \frac{1}{3}} = 10 + 3^{\frac{7}{3}} + 3^{\frac{5}{3}} - 3^{\frac{7}{3}} - 3^{\frac{5}{3}} = 10$

if x = 31/3 + 3 -1/3, then whatis the value of 3x3 - 9x ?rna) 12 b) 9 c)15 d) 10 how??

if x = 3^1/3+ 3 ^-1/3, thenwhatis the value of 3x³ - 9x ?
rn
a) 12 b) 9 c)15 d) 10 how??