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a, (a + b + c)^2 + (a - b - c)^2 +( b - c - a) ^2 + (c - a - b)^2
= (a + b + c)^2 + (a + b - c)^2 + (a - b - c)^2 + (a - b + c)^2
= (a + b)^2 + 2c(a + b) + c^2 + (a + b)^2 - 2c(a + b) + c^2 +
(a - b)^2 - 2c(a - b) + c^2 + (a - b)^2 + 2c(a - b) +c^2
= 2(a + b)^2 + 2c^2 + 2(a - b)^2 + 2c^2
= 2[(a + b)^2 + (a - b)^2] + 4c^2
=2(2a^2 + 2b^2) + 4c^2
= 4(a^2 + b^2 + c^2)
\(P=\frac{a^2}{\left(a-b\right)\left(a-c\right)}+\frac{b^2}{\left(b-a\right)\left(b-c\right)}+\frac{c^2}{\left(c-b\right)\left(c-a\right)}\)
\(P=\frac{a^2}{\left(a-b\right)\left(a-c\right)}-\frac{b^2}{\left(a-b\right)\left(b-c\right)}+\frac{c^2}{\left(c-b\right)\left(c-a\right)}\)
\(P=\frac{1}{a-b}.\frac{a^2\left(b-c\right)-b^2\left(a-c\right)}{\left(a-c\right)\left(b-c\right)}+\frac{c^2}{\left(c-b\right)\left(c-a\right)}\)
\(P=\frac{1}{a-b}.\frac{a^2b-a^2c-b^2a+b^2c}{\left(a-c\right)\left(b-c\right)}+\frac{c^2}{\left(c-b\right)\left(c-a\right)}\)
\(P=\frac{1}{a-b}.\frac{ab\left(a-b\right)-c\left(a-b\right)\left(a+b\right)}{\left(a-c\right)\left(b-c\right)}+\frac{c^2}{\left(c-b\right)\left(c-a\right)}\)
\(P=\frac{1}{a-b}.\frac{\left(a-b\right)\left(ab-ac-bc\right)}{\left(a-c\right)\left(b-c\right)}+\frac{c^2}{\left(b-c\right)\left(a-c\right)}\)
\(P=\frac{ab-ac-bc}{\left(a-c\right)\left(b-c\right)}+\frac{c^2}{\left(a-c\right)\left(b-c\right)}\)
\(P=\frac{ab-ac-bc+c^2}{\left(a-c\right)\left(b-c\right)}=\frac{a\left(b-c\right)-c\left(b-c\right)}{\left(a-c\right)\left(b-c\right)}=\frac{\left(a-c\right)\left(b-c\right)}{\left(a-c\right)\left(b-c\right)}\)
=> P = 1
Đáp số: P=1
\(P=-\frac{a^2}{\left(a-b\right)\left(c-a\right)}-\frac{b^2}{\left(a-b\right)\left(b-c\right)}-\frac{c^2}{\left(c-a\right)\left(b-c\right)}\)
\(=-\frac{a^2\left(b-c\right)+b^2\left(c-a\right)+c^2\left(a-b\right)}{\left(a-b\right)\left(b-c\right)\left(c-a\right)}\)
\(=-\frac{\left(a-b\right)\left(b-c\right)\left(a-c\right)}{\left(a-b\right)\left(b-c\right)\left(c-a\right)}=1\)
( a + b + c ) 2 = a2 + b2 + c2 + 2ab + 2bc + 2ac
( a + b - c ) 2 = a2 + b2 + c2 + 2ab - 2bc - 2ac
-2(a+b) = -2a2 - 2b2 - 4ab
thay vào a) thì sẽ được kết quả cuối là 2c2 thay c=-10 ta được kết quả là 200
câu b thì tương tự với ( a - b + c ) 2 = a2 + b2 + c2 - 2ab - 2bc + 2ac
( -a + b + c ) 2 = a2 + b2 + c2 - 2ab + 2bc - 2ac
thu gọn xong thay vô là ra