Question

if x is equal to 2 + root 3 find the value of x cube + 1 by x cube​

Answer 1

Topic :-

Algebraic Identities

Given :-

x = 2 + √3

To Find :-

x³ + 1/x³

Formula to be Used :-

a² - b² = ( a + b )( a - b )

( a + b )³ + ( a - b )³ = 2a³ + 6ab²

Solution :-

x = 2 + √3

1 = 4 - 3

1 = 2² - ( √3 )²

From mentioned formula,

1 = ( 2 + √3 )( 2 - √3 )

1 = x( 2 - √3 )

1 / x = ( 2 - √3 )

Now,

x³ + 1/x³

( 2 + √3 )³ + ( 2 - √3 )³

From mentioned formula,

2(2)³ + 6(2)(√3)²

2(8) + 12(3)

16 + 36

52

Answer :-

So, x³ + 1/x³ equals to 52.

Additional Formulae :-

( a + b )³ = a³ + b³ + 3ab( a + b )

( a - b )³ = a³ - b³ - 3ab( a - b )

Note :- Upon adding these two formulas; you can get above mentioned formula.