Question

Q.10
If x - 1/x = 3, find the value of : (i) x + 1/x​

Answer 1

Answer:

$\frac{x - 1}{x} = 3 \\ x - 1 = 3x \\ 3x - x + 1 \\ 2x + 1 \\ \frac{x + x + 1}{2x} \\ \frac{x + 1}{x} \\ hence \: it \: proved$

Answer 2

Answer:

±√13

Step-by-step explanation:

$(x-\frac{1}{x} )^{2} = 3^{2} \\x^{2}+ (\frac{1}{x} ) ^{2} -2 = 9\\x^{2}+ (\frac{1}{x} ) ^{2} = 11 .........(i)\\\\Let, \\(x+\frac{1}{x} ) = y\\(x+\frac{1}{x} )^{2} = y^{2} \\x^{2}+ (\frac{1}{x} ) ^{2} +2 =y^{2} \\11 + 2 = y^{2} \\y^{2} = 13$

y= ±√13

∴ x + 1/x​ = ±√13