If a^2 + 1/a^2 =18 then find : a-1/a

1.	If a^2 + 1/a^2 =18 then find : a-1/a
Answer» ANSWER: $a-\frac{1}{a}=\pm 4$ Step-by-step explanation: Given : $a^2+\frac{1}{a^2}=18$ To FIND : The value of $a-\frac{1}{a}$ ? Solution : Using IDENTITY, $(x-y)^2=x^2+y^2-2xy$ LET $x=a$ and $y=\frac{1}{a}$ Substitute in the identity, $(a-\frac{1}{a})^2=a^2+\frac{1}{a^2}-2\times a\times \frac{1}{a}$ $(a-\frac{1}{a})^2=18-2$ $(a-\frac{1}{a})^2=16$ TAKING root both side, $a-\frac{1}{a}=\pm 4$

Answer»

$a-\frac{1}{a}=\pm 4$