Question

if x+1/x = 3 find x2-1/x2

Answer 1

Answer:

X^2 - (1/x)^2 = 7.

Step-by-step explanation:

X + 1/x = 3

We know that (X+1/x)^2 = x^2 + (1/x)^2 + 2(x * 1/x)

=> (X+1/x)^2 = x^2 + (1/x)^2 + 2

Substituting value from (i) (3)^2 = x^2+(1/x)^2+2

= 9–2 = x^2-(1/x)^2

Ans. X^2 - (1/x)^2 = 7.

hope this answer will help you.

Answer 2

Answer:

3√5

Step-by-step explanation:

x+1/x=3

squaring both sides

x²+1/x²=7

We know,

(x-1/x)²=x²+1/x²-2

sbustituting X2+1/x² value above

We have, x-1/x =√5

We also know, x²-1/x²= (x+1/x) (x-1/x)

substituting the values we have

x²-1/x²=3√5