Question

if x=2+√3 then find the value of X²+1/X²
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Answer 1

Answer:

14

Step-by-step explanation:

x = 2+√3

1/x = 1/ 2+√3 × (2-√3)/(2-√3) = 2-√3

x+1/x = 2+√3 + 2-√3 = 4

(x+1/x)² = x² + 1/x² + 2(x)(1/x)

            = x² +1/x² + 2

4² = x² + 1/x² + 2

16 = x² + 1/x² + 2

14 = x² + 1/x²

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Answer 2

Answer:

Step-by-step explanation:

x=2 + √3

x² = (2+√3)² = 4+3+ 4√3   =  7+4√3

x² +1/x²  =   7+√3 +   1/7+√3

             =   7+ 4√3  +     1/7+4√3 * 7-4√3/7-4√3

             =   7+4√3  +   7-4√3 / (7)² - (4√3)²

               =  7+4√3   +   7-4√3 /49-48

               =7+4√3  +   7-4√3

                =  14