Find all the real solutions of the following equation by fir

Find all the real solutions of the following equation by first. 12y^2/3, 23y^1, 10 - 0 a. -4/9 - 25/16 b.-8/27 125/64 c.2/3 - 25/10 16. d. -8/27 - 25/16 e. -2/4 - 5/4 Use the power principle to solve the following radical equation

Solution

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12y ^ (2/3) + 23 y ^ (1/3) + 10 = 0

Let y^(1/3) = t

=> 12t^2 + 23t + 10 = 0

12t^2 + 15t + 8t + 10 = 0

3t (4t + 5) + 2 (4t + 5) = 0

(3t + 2) (4t + 5) = 0

t = -2/3 , -5/4

y ^ 1/3 = -2/3                                      y^1/3 = -5/4

y = -8/27                                             y = -125 / 64

i.e. Option D