Question

If a - 1/a = 8 and a is not equal to 0 , find 1) a+ 1/a and 2) a^2 - 1/a^2

Please tell the second answer!!!

Answer 1

so the answer for second part is -48

Answer 2

Answer:

1) $2\sqrt{17}$         2)$16\sqrt{17}$

Step-by-step explanation:

$(i)~a+\frac{1}{a}\\\\(a+\frac{1}{a})^2 - (a+\frac{1}{a})^2=4\\\\(a+\frac{1}{a})^2 - (8)^2 = 4\\\\(a+\frac{1}{a})^2 - 64 = 4\\\\(a+\frac{1}{a})^2 = 4 + 64\\\\(a+\frac{1}{a})^2 = 68\\\\(a+\frac{1}{a}) = \sqrt{68}\\\\(a+\frac{1}{a}) = \sqrt{4*17}\\\\(a+\frac{1}{a}) = 2\sqrt{17}$

$(ii)~a^2-\frac{1}{a^2}\\\\(a+\frac{1}{a})(a-\frac{1}{a})=a^2-\frac{1}{a^2}\\\\(2\sqrt{17})(8) = a^2-\frac{1}{a^2}\\\\2\sqrt{17} * 8 = a^2-\frac{1}{a^2}\\\\16\sqrt{17} = a^2-\frac{1}{a^2}$

Hope it helps you mate..

:)