Cho:a+b=s ;a.b =p
biểu diễn các biểu thức sau theo s và p
a,a2+b2 b,a3+ b3 c, a4 +b4
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NT
0
30 tháng 12 2016
Vì \(a+b+c=2016\Rightarrow a=2016-\left(b+c\right);b=2016-\left(a+c\right);c=2016-\left(a+b\right)\)
Ta có:\(S=\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b}\)
\(S=\frac{2016-\left(b+c\right)}{b+c}+\frac{2016-\left(a+c\right)}{a+c}+\frac{2016-\left(a+b\right)}{a+b}\)
\(S=\frac{2016}{b+c}-1+\frac{2016}{a+c}-1+\frac{2016}{a+b}-1\)
\(S=2016.\left(\frac{1}{b+c}+\frac{1}{a+c}+\frac{1}{a+b}\right)-3\)
\(S=2016.\frac{1}{2016}-3\)
\(S=-2\)
DT
2
28 tháng 9 2015
a) a2 + b2 = a2 + b2 + 2ab - 2ab = (a + b)2 - 2ab = s2 - 2p
b) a3 + b3 = (a + b)(a2 - ab + b2) = (a + b)(a2 + 2ab + b2 - 3ab) = (a + b).[(a + b)2 - 3ab] = s.(s2 - 3p) = s3 - 3ps
c) a4 + b4 = a4 + b4 + 4a2b2 - 4a2b2 = (a2 + b2)2 - 4(ab)2 = (s2 - 2p)2 - 4p2
= (s2 - 2p - 2p)(s2 - 2p + 2p) = s2.(s2 - 4p) = s4 - 4ps2
23 tháng 9 2021
\(1,\\ a,X=\left\{3;4\right\};\left\{2;3;4\right\};\left\{1;2;3;4\right\}\\ b,X=\left\{2;4\right\}\\ X=\left\{2\right\}\\ X=\left\{4\right\}\\ X=\varnothing\)
\(2,\\ a,A=\left\{-3;-2;0;1;2;3;4\right\}\\ B=\left\{0;1;2;3;4;6;9;10\right\}\\ b,A=\left\{1;2;3;4;5\right\}\\ B=\left\{1;2;3;6;9\right\}\)
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30 tháng 11 2021
Câu 2:
a: \(\Leftrightarrow x+2\in\left\{3;9\right\}\)
hay \(x\in\left\{1;7\right\}\)
TN
25 tháng 7 2018
\(a+b=132\)\(\left(1\right)\)
\(a-b=4\) \(\left(2\right)\)
lấy \(\left(1\right)-\left(2\right)\)ta có
\(a+b-a+b=132-4\)
<=> \(2b=128\)
<=> \(b=64\)
=> \(a=4+b=4+64=68\)
a, \(a^2+b^2=\left(a+b\right)^2-2ab\)
Thay a+b=s; ab vào đa thức trên ta được:
\(\left(a+b\right)^2-2ab=s^2-2p\)
b, \(a^3+b^3=\left(a+b\right)^3+3a^2b-3ab^2\)
\(=\left(a+b\right)^3-3ab.\left(a+b\right)\)
Thay a+b=s; ab=p Ta được:
\(\left(a+b\right)^3-3ab.\left(a+b\right)=s^3-3sp\)
c, \(a^4+b^4=\left(x^2+y^2\right)^2-2x^2y^2\)
\(=\left(s^2-2p\right)^2-2p^2=s^4-4s^2p+2p^2\)
CHÚC HỌC TỐT!!