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13 May 2017, 15:45
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I'm getting two different answers for the same problem when attempting different methods. Could anybody tell me what I'm doing wrong?
Problem: (x-1)^3<8
Method 1:
((x-1)^3)^1/3 < 8^1/3
x-1 < 2
Answer: x < 3
Method 2:
x^3 - 1^3 < 8
x^3 < 9
(x^3)^1/2 < 9^1/2
Answer: x^1.5 < 3
Problem: (x-1)^3<8
Method 1:
((x-1)^3)^1/3 < 8^1/3
x-1 < 2
Answer: x < 3
Method 2:
x^3 - 1^3 < 8
x^3 < 9
(x^3)^1/2 < 9^1/2
Answer: x^1.5 < 3
13 May 2017, 16:45
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At second method the following formula should work:
(a-b)^3=a^3-3a^2b+3ab^2-b^3
(x-1)^3=x^3-3x^2+3x-1
Sent from my SM-G920F using GMAT Club Forum mobile app
(a-b)^3=a^3-3a^2b+3ab^2-b^3
(x-1)^3=x^3-3x^2+3x-1
Sent from my SM-G920F using GMAT Club Forum mobile app
13 May 2017, 19:30
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eyerushh
I'm getting two different answers for the same problem when attempting different methods. Could anybody tell me what I'm doing wrong?
Problem: (x-1)^3<8
Method 1:
((x-1)^3)^1/3 < 8^1/3
x-1 < 2
Answer: x < 3
Method 2:
x^3 - 1^3 < 8
x^3 < 9
(x^3)^1/2 < 9^1/2
Answer: x^1.5 < 3
Problem: (x-1)^3<8
Method 1:
((x-1)^3)^1/3 < 8^1/3
x-1 < 2
Answer: x < 3
Method 2:
x^3 - 1^3 < 8
x^3 < 9
(x^3)^1/2 < 9^1/2
Answer: x^1.5 < 3
rencsee is right. Your method 2 is not correct.
\((x-1)^3 = x^3 - 3x^2+3x - 1 < 8\)
However, this method just makes the problem more complex. You should follow method 1.
