Question

if x+1/x=3 then find (x-1/2)^2

Answer 1

Answer:

x²+1/x² = 11

Explanation:

Given

x-1/x = 3---(1)

On Squaring equation (1), we get

=> (x-1/x)² = 3²

=> x²+1/x²-2*x*(1/x) = 9

/* By algebraic identity :

(a-b)² = a²+b²-2ab */

=> x²+1/x² - 2 = 9

=> x² + 1/x² = 9 +2

=> x² + 1/x² = 11

Therefore,

x²+1/x² = 11

Answer 2

Answer:

Given;

x+1/x=3

After Squaring the Equation

We obtained,

(x-1/x²) = 3²

x² + 1/x² -2 × x × (1/x)²

Algebric Identity,

(a - b)² = a² + b² - 2ab

x² + 1/x² - 2 = 9

x² + 1/x² = 9 + 2

x² + 1/x² = 11

Answer will be x² + 1/x² = 11.