Question

if x + 1/x = 1 ,

then, proved that
x³ = -1

Answer 1

Given

• x + 1/x = 1

To prove

• x³ = -1

Solution

Let's start with what's given ; x + 1/x = 1

Taking "x" as LCM :-

→ (x² + 1)/x = 1

→ x² + 1 = x ............. (1)

Now if we consider (a³ + b³) as (x³ + 1³) :-

• a³ + b³ = (a + b)(a² - ab + b²)

Now according to it :

→ x³ + 1³ = (x + 1)(x² - x + 1²)

→ x³ + 1 = (x + 1)(x² + 1 - x)

• x² + 1 = x [From (1)]

→ x³ + 1 = (x + 1)(x - x)

→ x³ + 1 = (x + 1) × 0

→ x³ + 1 = 0

→ x³ = - 1 [Hence proved]

Answer 2

Step-by-step explanation:

Refer to the attachment mate..........

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