If x½= 8, then (x⅓)²=?
Please answer this question. Its urgent
Answers
Answered by
21
*Answer:-
- 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.
Similar questions