if x = 1 + √ 2 , then what is the value of x 4 - 4 x 3 + 4 x 2 + 4 ?
answer x = 1 + √ 2 ∴ x 4 - 4 x 3 + 4 x 2 + 5 = x 2 ( x 2 - 4 x + 4 ) + 4 = x 2 ( x - 2 ) 2 + 4 = ( 1 + √ 2 ) 2 ( 1 + √ 2 - 2 ) 2 + 4 = ( √ 2 + 1 ) 2 ( √ 2 - 1 ) 2 + 4 = [ ( √ 2 ) 2 - ( 1 ) 2 ] 2 + 4 = ( 2 - 1 ) 2 = 1 + 4 = 5 correct option : c
add(multiply(power(add(1, sqrt(2)), const_2), power(subtract(add(1, sqrt(2)), 2), const_2)), 4)