Question

2y^2/3+ 11y^1/3 + 15 = 0

Answer 1

Answer: y=-27 y=-15.625

Explanation:

`\displaystyle\\2y^(2)/(3) +11y^(1)/(3) +15=0\\Let\ y^(1)/(3) =u\\Hence,\\2u^2+11u+15=0\\2u^2+6u+5u+15=0\\2u(u+3)+5(u+3)=0\\(u+3)(2u+5)=0\\u+3=0\\u=-3\\Hence,\\y^(1)/(3) =-3\\ Take\ both\ parts\ of\ the\ equation \ to \ the\ third\ power:\\(y^(1)/(3))^3=(-3)^3 \\y=(-3)(-3)(-3)\\y=-27\\2u+5=0\\2u+5-5=0-5\\2u=-5\\Divide\ both\ parts\ of\ the\ equation\ by\ 2:\\u=-2.5\\Hence,\\y=(-2.5)^3\\y=-15.625`

Answer 2

y=(-11-sqrt(241))/4=-6.631. or

y=(-11+sqrt(241))/4=1.131