If x= 2+√3, find the value of x^4 + 1/ x^4
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x = 2 + √3
1/x = (2 - √3)/(4 - 3) [by Rationalization]
1/x = 2 - √3
======================
Then,
x² + 1/x²
(2 + 3)² + (2 - 3)²
4 + 3 + 4√3 + 4 + 3 - 4√3
14
=================
(x^2 + 1/x^2) = 14
(x^4 + 1/x^4) = 14^2
x^4 + 1/x^4 = 196
i hope this will help you
(-:
1/x = (2 - √3)/(4 - 3) [by Rationalization]
1/x = 2 - √3
======================
Then,
x² + 1/x²
(2 + 3)² + (2 - 3)²
4 + 3 + 4√3 + 4 + 3 - 4√3
14
=================
(x^2 + 1/x^2) = 14
(x^4 + 1/x^4) = 14^2
x^4 + 1/x^4 = 196
i hope this will help you
(-:
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