Question

if x = 2+√3, then find the value of x^2 +1/x^2​

Answer 1

${\red{Hola!!}}$

Given:-

x = 2+√3

To find :- x²+1/x²

(2+√3)²+ 1/ (2+√3)²

=2²+√3²+2×2×√3+ 1/ 2²+√3²+2×2×√3

=4+3+4√3+ 1/4+3+4√3

=7+4√3 + 1/7+4√3

=(7+4√3)²+1/7+4√3

=[7²+(4√3)²+2×7×4√3]+1/7+4√3

=[49+(16×3)+56√3]+1/7+4√3

=(49+48+56√3+1)/7+4√3

=98+56√3/7+4√3

Hope it helps you...❤️✌️

Answer 2

Solution:-

$x=2+\sqrt{3} \\x^{2} =(2+\sqrt{3})^ {2} \\ x^{2} =4+3+4\sqrt{3} \\ x^{2} =7+4\sqrt{3} \\ \frac{1}{x^{2} } =\frac{1}{7+4\sqrt{3} }\\\frac{1}{x^{2} } =\frac{1}{7+4\sqrt{3} }*\frac{7-4\sqrt{3} }{7-4\sqrt{3} }  \\=\frac{7-4\sqrt{3} }{49-48} \\=7-4\sqrt{3}\\\\x^{2}+\frac{1}{x^{2} } =7+4\sqrt{3}  +7-4\sqrt{3}\\\\=14$

Answer=14