Question

x+1/x=3 then x²-1/x².

please find answer. ​

Answer 1

Answer:

3√5

Step-by-step explanation:

given,

x+1/x= 3 ...........(1)

=> x-1/x = √ (x+1/x)²- 4(x) (1/x)

=√ 3²-4

= √(9-4)

=> x-1/x = √5.........(2)

therefore, x²-1/x²

= (x+1/x) (x-1/x)

= 3.√5. from (1) and (2)

hence, x²-1/x² = 3√5

formula used:-

(1) A - B= √(A+B)²-4AB

(2) A²-B² = (A+B)(A-B)