Question

if x²+1/x² = 14, then what is the value of x + 1/x ?​

Answer 1

Answer:

(x-1/x)³ = x³-1/x³ - 3×x×1/x(1–1/x)

or (x-1/x)³ = x³-1/x³ - 3(1–1/x)

or (x-1/x)³ = 14 - 3(1–1/x) . . . . [Given, x³-1/x³ = 14]

Let x-1/x = a

Therefore a³ = 14 - 3a

or a³+3a-14 =0

or a³-2a²+2a²-4a+7a-14 =0

or a²(a-2) +2a(a-2) +7(a-2) =0

or (a-2)(a²+2a+7) =0

or a-2 = 0/(a²+2a+7)

or a = 2

So x-1/x = 2

Answer 2

Answer:

4

Step-by-step explanation:

x² + (1/x²) = 14

(formula --> (x + y)² = x² + y² + 2xy)

∴ (x + (1/x))² - 2x(1/x) = 14

(x + (1/x))² - 2 = 14

(x + (1/x))² = 16

square root on both sides,

x +(1/x) = 4