Question

If x=∛a+1 +∛a-1 , prove that x³ - 3ax² +3x =a
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∛a+1 -∛a-1

Answer 1

Answer:

x=∛a+1 +∛a-1

Applying componendo and dividendo rule , we get

{this rule states that if a/b = c/d ,then (a+b)/(a-b) = (c+d)/(c-d) }

(x+1)/(x-1) = (∛a+1) / (∛a-1)

cross mutiplying the eqn we get

ax^3 - x^3 + a - 1 + 3ax^2 - 3x^2 + 3ax - 3x = ax^3 + x^3  - 3x^2 - 3ax^2 + 3ax +3x - a - 1

solving the above equation we get

6ax^2 + 2a = 2x^3 + 6x

dividing the above equation by 2 we get

x³ - 3ax² +3x =a

Answer 2

QUESTION:

If x=∛a+1 +∛a-1

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∛a+1 -∛a-1 , prove that x³ - 3ax² +3x =a

hope it helped you