Question

If x = 2+√3, find the value of x^2 +1/x^2. [Use identity (a + b)^2 = a^2 + b^2+2ab]

Answer 1

Answer:

14

Step-by-step explanation:

Hello mate ( ´◡‿ゝ◡`)

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Given that,

x=2+√3 and find value of x²+1/x²

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All you need to do is substitute the value of x as I did below,

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x² + 1/x²

= (2 + √3)² + 1/(2 + √3)²

= [2² + 2(2)(√3) + (√3)²] + 1/[2² + 2(2)(√3) + (√3)²]

= (4 + 4√3 + 3) + 1/(4 + 4√3 + 3)

= (7 + 4√3) + 1/(7 + 4√3)

= (7 + 4√3)²/(7 + 4√3) + 1/(7 + 4√3)

= ((7 + 4√3)² + 1)/(7 + 4√3)

= (7² + 2(7)(4√3) + (4√3)² + 1)/(7 + 4√3)

= (49 + 56√3 + 48 + 1)/(7 + 4√3)

= (98 + 56√3)/(7 + 4√3)

= 14(7 + 4√3)/(7 + 4√3)

= 14

-> x²+1/x²=14

Hope you understood and have a great day