Question

If x-1/x = 7 , evaluate x^2 + 1/x^2 ,
x^4 + 1/x^4.

Answer 1

Solution :-

→ (x - 1/x) = 7

Squaring both sides we get,

→ (x - 1/x)² = 7²

using (a - b)² = a² + b² - 2ab in LHS ,

→ x² + 1/x² - 2 * x * 1/x = 49

→ x² + 1/x² - 2 = 49

→ x² + 1/x² = 49 + 2

→ x² + 1/x² = 51 (Ans.)

Now,

→ x² + 1/x² = 51

Squaring both sides we get,

→ (x² + 1/x²)² = 51²

using (a + b)² = a² + b² + 2ab in LHS ,

→ x⁴ + 1/x⁴ + 2 * x² * 1/x² = 2601

→ x⁴ + 1/x⁴ + 2 = 2601

→ x⁴ + 1/x⁴ = 2601 - 2

→ x⁴ + 1/x⁴ = 2599 (Ans.)

Answer 2

Answer:

Step-by-step explanation:

x-1/x=7

x-1=7x

6x=1

x=1/6

1/6^2 + 6^2

=> (1+36^2)/36

=>1297/36

1/6^4 + 6^4

=> (1+1296^2)/1296

=>46657/1296