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A Value Problem (Posted on 20070114) 

Given that, H^{3} H 1 = 0.
Determine analytically the exact value of:
(3H^{2}  4H)^{1/3} + H(2H^{2}+3H+2)^{1/4}

Submitted by K Sengupta

Rating: 4.0000 (1 votes)


Solution:

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By the problem;
H^3  H  1 = 0
Or, H = H^3  1
Or, H+1 = H^3
So, 3*H^2  4H
= 3*H^2  3H  (H^3 1)
= 1  3H + 3*H^2  H^3
= (1H)^3
Now, 2*H^2 +3H +2
= H^2 + (H^2 + H) + 2(H+1)
= H^2 + H(H^3) + 2*H^3
= H^4 + 2*H^3 + H^2
= (H^2)[(H+1)^2]
= H^2*H^6
= H^8
Therefore, the given expression is
= 1  H + H^3
= 1  H + 1 + H
= 2
Consequently, the required value of the expression is 2.

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