Question

If x-1/x=3/2, find the value of x+1/x​

Answer 1

Given, x+1/x = 9 , Squaring both sides

(x+1/x)² = 81 ……………………………………………………..(1)

Now we have

(x- 1/x)² = x² - 2.x.1/x + (1/x)² = x² - 2+ 1/x²

Or, (x- 1/x)² = x² + 2 -2 - 2+ 1/x² (Adding and subtracting 2)

Or, (x- 1/x)² = x² + 2.1 - 4+ 1/x² = x² + 2.x.1/x - 4+ 1/x²

= (x² + 2.x.1/x + 1/x²) - 4 = (x+1/x)² - 4

Substituting for (x+1/x)² from (1),

(x- 1/x)² = 81 - 4 = 77 , Taking square root of both sides

⇒ x- 1/x = ±77½ or ±8.775 (rounded to third decimal) (Answer)

Answer 2

Answer:

1/2

Step-by-step explanation:

x-1/x=3/2

2(x-1)=3x

2x-2=3x

x=-2

x+1/x=(-2+1)/-2=-1/-2=1/2