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(a)ifα andβ are the roots of the equation x²+px+q=0,expressα³+β³and(α-β²)(β-α²) in terms of p and q(計到α³+β³=-p³+3pq and (α-β²)(β-α²)=p³-3pq+q²+q
(b)Reduce that the condition for one root of the equation to be the square of the other is p³-3pq+q²+q=0（呢條唔識)
中四amath1題
2008-10-25 3:10 am
回答 (5)
2008-10-25 5:27 am
2008-10-29 4:57 am
(b) Let the 2 roots be m and n.
Since (m - n^2)(n - m^2) = p^3 - 3pq + q^2 + q.......(1)
For the condition one root to be the square of the other, that is
m = n^2 that is (m-n^2) = 0 or
n = m^2 that is (n - m^2) = 0. That is (1) = 0,
so p^3 -3pq + q^2 + q = 0 is the condition.
Since (m - n^2)(n - m^2) = p^3 - 3pq + q^2 + q.......(1)
For the condition one root to be the square of the other, that is
m = n^2 that is (m-n^2) = 0 or
n = m^2 that is (n - m^2) = 0. That is (1) = 0,
so p^3 -3pq + q^2 + q = 0 is the condition.
2008-10-29 4:54 am
(b) Let the 2 roots be m and n.
Since (m - n^2)(n - m^2) = p^3 - 3pq + q^2 + q.......(1)
For the condition one root to be the square of the other, that is
m = n^2 that is (m-n^2) = 0 or
n = m^2 that is (n - m^2) = 0. That is (1) = 0,
so p^3 -3pq + q^2 + q = 0 is the condition.
Since (m - n^2)(n - m^2) = p^3 - 3pq + q^2 + q.......(1)
For the condition one root to be the square of the other, that is
m = n^2 that is (m-n^2) = 0 or
n = m^2 that is (n - m^2) = 0. That is (1) = 0,
so p^3 -3pq + q^2 + q = 0 is the condition.
2008-10-25 6:45 am
(b) Let the 2 roots be m and n.
Since (m - n^2)(n - m^2) = p^3 - 3pq + q^2 + q.......(1)
For the condition one root to be the square of the other, that is
m = n^2 that is (m-n^2) = 0 or
n = m^2 that is (n - m^2) = 0. That is (1) = 0,
so p^3 -3pq + q^2 + q = 0 is the condition.
Since (m - n^2)(n - m^2) = p^3 - 3pq + q^2 + q.......(1)
For the condition one root to be the square of the other, that is
m = n^2 that is (m-n^2) = 0 or
n = m^2 that is (n - m^2) = 0. That is (1) = 0,
so p^3 -3pq + q^2 + q = 0 is the condition.
2008-10-25 5:57 am
(b) Let the 2 roots be m and n.
Since (m - n^2)(n - m^2) = p^3 - 3pq + q^2 + q.......(1)
For the condition one root to be the square of the other, that is
m = n^2 that is (m-n^2) = 0 or
n = m^2 that is (n - m^2) = 0. That is (1) = 0,
so p^3 -3pq + q^2 + q = 0 is the condition.
Since (m - n^2)(n - m^2) = p^3 - 3pq + q^2 + q.......(1)
For the condition one root to be the square of the other, that is
m = n^2 that is (m-n^2) = 0 or
n = m^2 that is (n - m^2) = 0. That is (1) = 0,
so p^3 -3pq + q^2 + q = 0 is the condition.
收錄日期: 2021-04-23 20:35:09
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https://hk.answers.yahoo.com/question/index?qid=20081024000051KK01385