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Solution


Q.

The real roots of the equation x2/3 + x1/3- 2 = 0  are:

(i) 1     (ii) -8     (iii) -1     (iv) 8

 

Choose the correct option from the following:
1 (i) and (ii)  
2 (i) and (iv)  
3 (iii) and (iv)  
4 (ii) and (iii)       

Ans.

(1)

Given equation is x2/3 + x1/3- 2 = 0 

⇒ t² + t - 2 = 0     (Take x1/3 = t)

⇒ t² + 2t - t - 2 = 0

⇒ t(t + 2) - 1(t + 2) = 0     ⇒ (t + 2)(t - 1) = 0

The roots of above equation are t = 1 and t = -2.

If t = 1, then x = 1.

If t = -2, then x = -8.