2 questions only =]

2009-08-14 5:39 am

1)
Factorize: 3a(b^2)(c^2)-127(a^3)
i try to factorize it into the following steps
3a(b^2)(c^2)-147(a^3)+20(a^3)
3a[(bc)^2-(7a)^2]+20(a^3)
3a(bc+7a)(bc-7a)+20(a^3)
a[3(bc+7a)(bc-7a)+20(a^2)] <---- is this fully factorized? [Yes/No]

2)

a^2+b^2=6ab, find the possible value(s) of (a+b)/(a-b) <---plz HELP!!!!

更新1:

if the first question's answer is NO, please give the correct steps and answer, thx a lot!!

更新2:

But did you copy the question correctly? The answer looks a bit odd. its so odd, that is why i need to ask ma!>< how do you make (^2) directly?

回答 (1)

用戶9112

2009-08-14 6:02 am

✔ 最佳答案

1) Your factorization is not correct.
3ab2c2 – 127a3
= 3a(b2c2 – 127a2/3)
= 3a{(bc)2 – [√(127/3)a]2}
= 3a[bc + √(127/3)a][bc – √(127/3)a]
But did you copy the question correctly? The answer looks a bit odd.
2)
a2 + b2 = 6ab
a2 + 2ab + b2 = (a + b)2 = 8ab
a2 – 2ab + b2 = (a – b)2 = 4ab
(a + b)2 / (a – b)2 = 8ab / 4ab = 2
(a + b) / (a – b) = √2 or - √2

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