Question

factorise it
x⅔ +x⅓ -2=0​

Answer 1

Answer:

What is the value of x if x⅔+x⅓–2=0? How can I find the value so easily?

Answer: x = 1, x =-8

Proof:

The given equation

x⅔ + x⅓ - 2 = 0

can be written as (x⅓)² + x⅓ - 2 = 0 ………………………………………………….(1)

If y = x⅓ then (x⅓)² = y² and (1) →

y² + y - 2 = 0

Or, (y² - 1) + y - 1 = 0

Factorising the quantity within brackets,

(y+1) (y-1) + (y-1) = 0

Or, (y-1) (y+1 + 1) =0 [the common factor y-1 is taken out]

Or, (y - 1) (y + 2) = 0

Or, y - 1 = 0, y + 2 = 0

⇒ y = 1 , y = -2

⇒ x⅓ = 1, x⅓ = -2 (∵ y = x⅓)

Cubing (x⅓)³ = 1³ , (x⅓)³ = (-2)³

⇒ x = 1, x = -8 (Answer)

Verification:

x = 1

L.H.S. of (1) = (x⅓)² + x⅓ - 2 = (1⅓)² + 1⅓ - 2 = 1²+ 1 - 2 = 1² + 1 - 2 = 1+1 = 0 = R.H.S.

x = -8

L.H.S. of (1) = (-8⅓)² + (-8)⅓ - 2 = (-2)² - 2 - 2 = 4 - 2 - 2 = 4 - 4 = 0 = R.H.S.