Question

if x^2-x+1=0, x^3=?
please give me the ans.

Answer 1

Step-by-step explanation:

x={1±√(1-4)}/2

x= {1+√-3}/2

x³={1+√-3}³/8

Answer 2

Required Answer:-

Given:

• x² - x + 1 = 0

To Find:

• x³ = ?

Solution:

We have,

➡ x² - x + 1 = 0 . . .(i)

➡ x² - x = -1 . . .(ii)

Multiplying equation (i) by x, we get,

➡ x³ - x² + x = 0

➡ x³ = x² - x

From (ii),

➡ x³ = -1

★ Hence, the value of x³ is 1.

Another approach,

We have,

➡ x² - x + 1 = 0

Now,

➡ x³ = x³

➡ x³ = x³ + 1 - 1

➡ x³ = (x³ + 1) - 1

➡ x³ = (x + 1)(x² - x + 1) - 1 [Using identity a³ + b³ = (a + b)(a² - ab + b²)]

As x² - x + 1 = 0, So,

➡ x³ = (x + 1) × 0 - 1

Any number multiplied by 0 gives 0. So,

➡ x³ = 0 - 1

➡ x³ = -1.

★ Hence, the value of x³ is -1.

Answer:

• x³ = -1.