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cho a,b,c khac nhau doi mot va 1/a+1/b+1/c=0.rut gon cac bieu thuc
N=bc/a^2+2bc+CA/B^2+2AC+AB/C^2+2AB
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\(\left(a+b-c\right)^2-\left(a-c\right)^2-2ab+2bc\)
\(=a^2+b^2+c^2+2ab-2ac-2bc-a^2+2ac-c^2-2ab+2bc\)
\(=b^2\)
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\(a,\)\(2\left(x-y\right)\left(x+y\right)+\left(x-y\right)^2+\left(x+y\right)^2.\)
\(=\left[\left(x-y\right)+\left(x+y\right)\right]^2=\left(x-y+x+y\right)^2=x^2\)
\(b,\)\(\left(2x-3\right)\left(4x^2+6x+9\right)-\left(54+8x\right)\)
\(=8x^2-27-54-8x=8x^2-8x-81\)
\(c,\)\(\left(3x+y\right)\left(9x^2-3xy+y^2\right)-\left(3x-y\right)\left(9x^2+3xy+y^2\right)\)
\(=27x^3+y^3-\left(27x^3-y^3\right)=2y^3\)
\(d,\)\(\left(a+b+c\right)^2-\left(a-c\right)^2-2ab+2bc\)
\(=a^2+b^2+c^2+2ab+2bc+2ac-a^2+2ac-c^2-2ab+2bc\)
\(=b^2+4bc+4ac\)
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Ta có : (a + b - c)2 + (a - b + c)2 - 2(b - c)2
= a² + b² + c² + 2ab - 2bc - 2ca + a² + b² + c² + 2ca - 2ab - 2bc - 2(b2 - 2bc + c2)
= a² + b² + c² + 2ab - 2bc - 2ca + a² + b² + c² + 2ca - 2ab - 2bc - b2 + 2bc - c2
= 2a2 + b2 + c2 - 2bc
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(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)
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\(\left(a+b-c\right)^2-\left(a-c\right)^2-2ab+2bc\)
\(=\left(a-c\right)^2+2b\left(a-c\right)+b^2-\left(a-c\right)^2-2ab+2bc\)
\(=2b\left(a-c\right)+b^2-2ab+2bc\)
\(=2ab-2bc+b^2-2ab+2bc=b^2\)