Question

if x=3+2 root 2 , evaluate x+1/x and x^2+1/x^2​

Answer 1

Answer:

Step-by-step explanation:

1/x=3-2√2

X+1/x=3+2√2+3-2√2=6

X^2+1/x^2=(x+1/x)^2-2.x.1/x=6^2-2=34

Answer 2

Answer:

Hey Mate!!

x = 3 + 2√2

⇢ 1/x = 1/(3 + 2√2)

⇢ 1/x = (3 - 2√2)/[(3 + 2√2)(3 - 2√2)]

⇢ 1/x = (3 - 2√2)/[3² + (2√2)²]

⇢ 1/x = (3 - 2√2)/(9 - 8)

⇢ 1/x = (3 - 2√2)/1

⇢ 1/x = 3 - 2√2

⇝ x + 1/x

⇝ 3 + 2√2 + 3 - 2√2

⇝ 6

x² = (3 + 2√2)²

⇢ x² = 3² + 2(3)(2√2) + (2√2)²

⇢ x² = 9 + 12√2 + 8

⇢ x² = 17 + 12√2

1/x² = 1/(17 + 12√2)

⇢ 1/x² = (17 - 12√2)/[(17 + 12√2)(17 - 12√2)]

⇢ 1/x² = (17 - 12√2)/[17² - (12√2)²]

⇢ 1/x² = (17 - 12√2)/(289 - 288)

⇢ 1/x² = (17 - 12√2)/1

⇢ 1/x² = 17 - 12√2

x² + 1/x²

⇝ 17 + 12√2 + 17 - 12√2

⇝ 34