Question

Please help me by solving these questions

Answer 1

Answer:

The answer is given below.

Step-by-step explanation:

x + $\frac{1}{x}$ = 4

(a) $x$ - $\frac{1}{x}$ = ?

 =  (x − 1/x)² = (x + 1/x)² - 4 * x * 1/x

=> (x − 1/x)² = 4² − 4

=> (x − 1/x)² = 12

=> (x − 1/x) = ± √(12)

=> (x − 1/x) = ± 2√(3) ===> (Ans)

(b) x² + 1/x²

= (x + 1/x)² = 4²

= x² + 1/x² +2×x×1/x = 16

= x² + 1/x² + 2 = 16

= x² + 1/x² = 14

(c) x + 1/x = 4 → ( x + 1/x)² = 16 → x² + 1/x² + 2 = 16 → x² +1/x² = 14

Now,

x² + 1/x² = 14 → ( x² + 1/x²)² = 196 → x⁴ + 1/x⁴ + 2 = 196 → x⁴ +1/x⁴ = 194.