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Originally Posted by pornclerk
I plugged in the values and did all of the correct math. Tell me what algebra i did wrong and then say it is wrong.
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(7x-2)^1/3 + (7x+5)^1/3 = 3
=> [(7^1/3)^3)(x^1/3)^3 - (2^1/3)^3)] + [(7^1/3)^3(x^1/3)^3 + (5^1/3)^3) = 3^3
Here you assume that (a + b)^n = a^n + b^n which it is not. Unless n = 1. Which it isn't in this case.
You also perform the ^ operation term by term on the left hand side of the equation, which is wrong, but that is probably connected to the previous erroneous assumption.
=> x = 12/7
Now let's check the answer:
[7(12/7) - 2]^1/3 + [7(12/7) + 5]^1/3 = 3
=> (12-2)^1/3 + (12+5)^1/3 = 3
=> [(10)^1/3]^3 + [(17)^1/3]^3 = 3^3
And here you do the ^3 operation term-by-term on the left hand side again, which is wrong. You make the same mistake when you check the answer as when you solve the equation, that's why your answer looks good to you.
Let's check this for real.
(7*12/7-2)^1/3 + (7*12/7+5)^1/3 = 10^1/3 + 17^1/3 = {Punch in on the ol' calculator.} = 2.1544 + 2.57128 > 3 So it's wrong.
Lesson: "Raise to the power of" does
not behave like "multiply with".