Question

if x=2+2⅓+2⅔, then x³- 6x²+6x+2 is equal to​

Answer 1

Answer:

If x=2+2(1/3)+2(2/3)

then the value of x^3-6x^2+ 6x

Step-by-step explanation:

sorry I have no explanation

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Answer 2

$\large\underline{\sf{Solution-}}$

Given that

$\rm :\longmapsto\:x = 2 + {\bigg(2\bigg) }^{\dfrac{1}{3} } + {\bigg(2\bigg) }^{\dfrac{2}{3} }$

$\rm :\longmapsto\:x - 2= {\bigg(2\bigg) }^{\dfrac{1}{3} } + {\bigg(2\bigg) }^{\dfrac{2}{3} } - - - (1)$

Cubing both sides, we get

$\rm :\longmapsto\:(x - 2)^{3} = \bigg( {\bigg(2\bigg) }^{\dfrac{1}{3} } + {\bigg(2\bigg) }^{\dfrac{2}{3} } \bigg)^{3}$

$\rm :\longmapsto\: {x}^{3} - {2}^{3} - 3(x)(2)(x - 2) = 2 + 4 + 3(2)^{ \frac{1}{3} } {(2)}^{ \frac{2}{3}}\bigg( {\bigg(2\bigg) }^{\dfrac{1}{3} } + {\bigg(2\bigg) }^{\dfrac{2}{3} } \bigg)$

$\: \: \: \: \: \red{\bigg \{ \because \: {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y)\bigg \}}$

$\rm :\longmapsto\: {x}^{3} - 8 - 6x(x - 2) = 2 + 4 + 3 \times 2 \times (x - 2)$

$\rm :\longmapsto\: {x}^{3} - 8 - 6 {x}^{2} + 12x = 6 + 6 (x - 2)$

$\rm :\longmapsto\: {x}^{3} - 8 - 6 {x}^{2} + 12x = 6 + 6x -12$

$\rm :\longmapsto\: {x}^{3} - 8 - 6 {x}^{2} + 12x = 6x -6$

$\rm :\longmapsto\: {x}^{3} - 6 {x}^{2} + 12x - 6x = -6 + 8$

$\rm :\longmapsto\: {x}^{3} - 6 {x}^{2} + 6x = 2$

On adding 2 both sides, we get

$\rm :\longmapsto\: {x}^{3} - 6 {x}^{2} + 6x + 2= 2 + 2$

$\rm :\longmapsto\: {x}^{3} - 6 {x}^{2} + 6x + 2= 4$

More Identities to know:

• (a + b)² = a² + 2ab + b²

• (a - b)² = a² - 2ab + b²

• a² - b² = (a + b)(a - b)

• (a + b)² = (a - b)² + 4ab

• (a - b)² = (a + b)² - 4ab

• (a + b)² + (a - b)² = 2(a² + b²)

• (a + b)³ = a³ + b³ + 3ab(a + b)

• (a - b)³ = a³ - b³ - 3ab(a - b)