Question

x = 2 + 2⅓ + 2⅔ , ƒıη∂ тнє ѵαłυє σƒ x³- 6x² + 6x - 2
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sσłѵє тнıs ρяσвłєм ıƒ yσυ sσłѵє тнıs тнєη yσυ cαη gєт
α мαяk σƒ вяαıηłıєsт αη∂ 50 тнαηks


тıρ -: {∂ση'т cσρy ƒяσм gσσgłє}​

Answer 1

Answer:

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x³ - 6x² + 6x = 2

Given---> x = 2 + 2²/³ + 2¹/³

To find---> Value of x³ - 6x² + 6x

Solution---> We know that,

( a + b )³ = a³ + b³ + 3ab ( a + b ) , and

(a - b )³ = a³ - b³ - 3ab ( a - b )

Now, x = 2 + 2²/³ + 2¹/³

=> x - 2 = 2²/³ + 2¹/³

Cubing both sides , we get

=> ( x - 2 )³ = ( 2²/³ + 2¹/³ )³

Now applying above identity , we get

=> x³ - 8 - 3 (x) ( 2 ) (x - 2 ) = (2²/³)³ + (2¹/³)³

+ 3 × 2¹/³ 2²/³ (2¹/³ + 2²/³ ) We have a law of exponent

( aᵐ )ⁿ = aᵐⁿ , applying it here , we get

=> x³ - 8 -6x(x - 2 ) = 2² + 2¹ + 3 × 2¹ ( x - 2 )

=> x³ - 8 - 6x² + 12x = 4 + 2 + 6x - 12

=> x³ - 6x² + 12x - 8 = 6x - 6

=> x³ - 6x² + 12x - 6x -8 + 6 = 0

=> x³ - 6x² + 6x - 2 = 0

=> x³ - 6x² + 6x = 2

${\mathfrak{{☆ \:  I  \: hope \:  its  \: help  \: you \:  ☆}}}$

Answer 2

Explanation:

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