Question

X-1/x
$x - 1 \x$
X2+1/x2=27
​

Answer 1

Question :

Find x - 1/x if x² + 1/x² = 27 .

Answer :

x - 1/x = 5

Solution :

• Given : x² + 1/x² = 27
• To find : x - 1/x = ?

Now ,

Let's consider the identity

(a - b)² = a² + b² - 2ab and putting a = x , b = 1/x in the given identity , we get ;

=> (x - 1/x)² = x² + (1/x)² - 2•x•(1/x)

=> (x - 1/x)² = x² + 1/x² - 2

=> (x - 1/x)² = 27 - 2

=> (x - 1/x)² = 25

=> x - 1/x = √25

=> x - 1/x = 5

Hence , x - 1/x = 5 .