Question

Please try this above attached sample.
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Answer 1

Answer:

0

Step-by-step explanation:

⇒ x = 1 / ( 2 + √3 )

Rationalising the denominator

⇒ x = ( 2 - √3 ) / ( 4 - 3 )

⇒x = 2 - √3

Squaring on both sides

⇒ x² = ( 2 - √3 )²

⇒ x² = 2² + ( √3 )² - 2( 2 )( √3 )

⇒ x² = 4 + 3 - 4√3

⇒ x² = 7 - 4√3

Now we will calculate the given polynomial

x³ - x² - 11x + 3

= x² ( x - 1 ) - 11x + 3

= ( 7 - 4√3 )( 2 - √3 - 1 ) - 11( 2 - √3 ) + 3

= ( 7 - 4√3 )( 1 - √3 ) - 22 + 11√3 + 3

= 7( 1 - √3 ) - 4√3( 1 - √3 ) - 19 + 11√3

= 7 - 7√3 - 4√3 + 12 - 19 + 11√3

= 19 - 12 - 11√3 + 12 - 19 + 11√3

= 0

Therefore the value of the given polynomial is 0.

Answer 2

Answer:

Answer:

0

Step-by-step explanation:

⇒ x = 1 / ( 2 + √3 )

Rationalising the denominator

⇒ x = ( 2 - √3 ) / ( 4 - 3 )

⇒x = 2 - √3

Squaring on both sides

⇒ x² = ( 2 - √3 )²

⇒ x² = 2² + ( √3 )² - 2( 2 )( √3 )

⇒ x² = 4 + 3 - 4√3

⇒ x² = 7 - 4√3

Now we will calculate the given polynomial

x³ - x² - 11x + 3

= x² ( x - 1 ) - 11x + 3

= ( 7 - 4√3 )( 2 - √3 - 1 ) - 11( 2 - √3 ) + 3

= ( 7 - 4√3 )( 1 - √3 ) - 22 + 11√3 + 3

= 7( 1 - √3 ) - 4√3( 1 - √3 ) - 19 + 11√3

= 7 - 7√3 - 4√3 + 12 - 19 + 11√3

= 19 - 12 - 11√3 + 12 - 19 + 11√3

= 0

Therefore the value of the given polynomial is 0.