Tính :A = y(x−y)(y−z) +z(y−z)(z−x) +x(z−x)(x−y) B = x+z(x−y)(y−z) −x+y(x−z)(y−z) −y+z(x−y)(x−z) C...
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Tính :
A = y(x−y)(y−z) +z(y−z)(z−x) +x(z−x)(x−y)
B = x+z(x−y)(y−z) −x+y(x−z)(y−z) −y+z(x−y)(x−z)
C =1a−b +1a+b +2aa2+b2 +4a3a4+b4 +8a7a8+b8
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15 tháng 3 2021
b) Ta có: \(a\left(b^2-c^2\right)+b\left(c^2-a^2\right)+c\left(a^2-b^2\right)\)
\(=ab^2-ac^2+bc^2-ba^2+ca^2-cb^2\)
\(=\left(ab^2-cb^2\right)+\left(ca^2-c^2a\right)+\left(bc^2-ba^2\right)\)
\(=b^2\left(a-c\right)+ca\left(a-c\right)+b\left(c^2-a^2\right)\)
\(=\left(a-c\right)\left(b^2+ca\right)-b\left(a-c\right)\left(a+c\right)\)
\(=\left(a-c\right)\left(b^2+ca-ba-bc\right)\)
\(=\left(a-c\right)\left[b\left(b-a\right)+c\left(a-b\right)\right]\)
\(=\left(a-c\right)\left[b\left(b-a\right)-c\left(b-a\right)\right]\)
\(=\left(a-c\right)\left(b-a\right)\left(b-c\right)\)
4 tháng 10 2019
a) A = x(y - z) + 2(z - y) = x(y - z) - 2(y - z) = (x - 2)(y - z) = (2 - 2)(1,007 - (-0,006)] = 0
b) B = 2x(y - z) + (z - y)(x + t) = 2x(y - z) - (y - z)(x + t) = (2x - x - t)(y - z) = (x - t)(y - z) = [18,3 - (-31,7)](24,6 - 10,6) = 50.14 = 700
c) C = (x - y)(y + z) + y(y - x) = (x - y)(y + z) - y(x - y) = (x - y)(y + z - y) = (x - y).z = (0,86 - 0,26).1,5 = 0,6.1,5 = 0,9
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10 tháng 2 2017
a) \(\left(x-y\right)-\left(x-z\right)=\left(z+x\right)-\left(y+x\right)\)
BL:
Ta có: \(\left(x-y\right)-\left(x-z\right)\)
\(=x-y-x+z\)
\(=z+x-y-x\)
\(=\left(z+x\right)-\left(y+x\right)\)
\(\Rightarrow\) \(\left(x-y\right)-\left(x-z\right)=\left(z+x\right)-\left(y+x\right)\)
b) \(\left(x-y+z\right)-\left(y+z-x\right)-\left(x-y\right)=\left(z-y\right)-\left(z-x\right)\)
BL:
Lại có: \(\left(x-y+z\right)-\left(y+z-x\right)-\left(x-y\right)\)
\(=x-y+z-y-z+x-x+y\)
\(=\left(x-y-x+y\right)+\left(z-y\right)-\left(z-x\right)\)
\(=\left(z-y\right)-\left(z-x\right)\)
\(\Rightarrow\) \(\left(x-y+z\right)-\left(y+z-x\right)-\left(x-y\right)=\left(z-y\right)-\left(z-x\right)\)
c) \(a\left(b+c\right)-b\left(a-c\right)=\left(a+b\right)c\) BL: Ta lại có: \(a\left(b+c\right)-b\left(a-c\right)=\left(a+b\right)c\) \(=ab+ac-ba+bc\) \(=\left(ab-ba\right)+\left(ac+bc\right)\) \(=0+\left(a+b\right)c\) \(=\left(a+b\right)c\) \(\Rightarrow\) \(a\left(b+c\right)-b\left(a-c\right)=\left(a+b\right)c\) \(\rightarrow\) đpcm.