IIT JEE , AIEEE Forum - Mathematics , Algebra

computer001

it is of the form (a+b)^1/3 + (a-b)^1/3...write this as (a+b + a-b)/{(a+b)^2/3 + (a-b)^2/3 -(a^2-b^2)^1/3} =
2a/{ {(a+b)^1/3 +(a-b)^1/3}^2 -3(a^2-b^2)^1/3}

(a^2-b^2)^1/3=(343)^1/3=7 v get...
consider (a+b)^1/3 + (a-b)^1/3=x..
from the prev equtaion v get this eqn:
x^3-21x=90...this will have 3 soln..one is ob 6..
so the eqn is (x-6)(x^2 + 6x +15) the quad has no real soln.. hence 6 is only real soln ..
so(a+b)^1/3 + (a-b)^1/3=6..

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