Question

if x-1/6 =7 then find x-1/x^2​

Answer 1

Correct Question :-

if (x - 1/x) = 7 , find (x² - 1/x²) ?

Solution :-

→ (x - 1/x) = 7

Squaring Both sides we get,

→ (x - 1/x)² = 7²

→ x² + 1/x² - 2 * x * 1/x = 49

→ x² + 1/x² - 2 = 49

→ x² + 1/x² = 51

Now Adding 2 both sides we get,

→ x² + 1/x² + 2 = 51 + 2

→ x² + 1/x² + 2 * x * 1/x = 53

→ (x + 1/x)² = 53

Square - root Both sides now,

→ (x + 1/x) = √53

Therefore,

→ (x² - 1/x²)

→ (x - 1/x)(x + 1/x)

→ 7 * √53

→ 7√53 (Ans.)