Question

plz help me to solve no. 10. equation of rational number of understanding mathematics class9 ICSE ml agarwal​

Answer 1

$x = 5 - 2 \sqrt{6} \\ \frac{1}{x} = \frac{1}{5 - 2 \sqrt{6} } \\ by \: rationalizing \: denominator \: we \:get \\ \frac{1}{x} = 5 + 2 \sqrt{6} \\ x + \frac{1}{x} = 10 \\ ( {x + \frac{1}{x} })^{2} = 100 \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 100 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 98$