Question

If x=3+2 root 2 find the value of x2+1/x2 with solution pls

Answer 1

Answer:

34

Step-by-step explanation:

⇒ x = 3 + 2√2

⇒ (1/x) = 1/(3 + 2√2)

     Multiply as well as divide RHS by 3 - 2√2

⇒ 1/x = (3 - 2√2)/(3 + 2√2)(3 - 2√2)

⇒ 1/x = (3 - 2√2)/(3² - (2√2)² )  {(a+b)(a-b)=a² - b²}

⇒ 1/x = (3 - 2√2)/( 9 - 8)

⇒ 1/x = 3 - 2√2

       Therefore,

⇒ x^2 + 1/x^2

⇒ (3 + 2√2)^2 + (3 - 2√2)^2

⇒ 9 + 8 + 12√2 + 9 + 8 - 12√2

⇒ 9 + 8 + 9 + 8

⇒ 34