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a,A=5x2z-10xyz+5y2z
=5z(x2-2xy+y2)
=5z(x-y)2
Thay x=124,y=24,z=2 vào A ta được:
A=5.2(124-24)2=10.1002=10000
b,B=2x2+2y2-x2z+z-y2z-2
=2(x2+y2)-z(x2+y2)+(z-2)
=(2-z)(x2+y2)-(2-z)
=(2-z)(x2+y2-1)
Thay x=1,y=1,z=-1 vào B
B=(2+1)(12+12-1)=3
c, C=x2-y2+2y-1
=x2-(y2-2y+1)
=x2-(y-1)2
=(x-y+1)(x+y-1)
=(75-26+1)(75+26-1)
=50.100=5000
\(A=5x^2z-10xyz+5y^2z=5z\left(x^2-2xy+y^2\right)=5z\left(x-y\right)^2\)
Thay x = 124, y = 24, z = 2 vào A, ta có:
\(5\times2\times\left(124-24\right)^2=10\times100^2=10\times10000=100000\)
Vậy A = 10 000 khi x = 124, y = 24, z = 2.
\(B=2x^2+2y^2-x^2z-y^2z+z-2=2\left(x^2+y^2-1\right)-z\left(x^2+y^2-1\right)=\left(2-x\right)\left(x^2+y^2-1\right)\)
Thay x = 1, y = 1, z = - 1 vào B, ta có:
\(B=\left[2-\left(-1\right)\right]\left(1^2+1^2-1\right)=3\times1=3\)
Vậy B = 3 khi x = 1, y = 1, z = - 1.
\(\dfrac{1}{2}\left(6x-2y\right)\left(3x+y\right)=\dfrac{1}{2}.2\left(3x-y\right)\left(3x+y\right)=9x^2-y^2\)
\(\left(\dfrac{2}{3}z-\dfrac{2}{5}x\right)\left(\dfrac{1}{3}z+\dfrac{1}{5}x\right).\dfrac{1}{2}=\left(\dfrac{1}{3}z-\dfrac{1}{5}x\right)\left(\dfrac{1}{3}z+\dfrac{1}{5}z\right).2.\dfrac{1}{2}=\dfrac{1}{9}z^2-\dfrac{1}{25}x^2\)
\(\left(5y-3x\right).\dfrac{1}{4}\left(12x+20y\right)=\left(5y-3x\right)\left(5y+3x\right).4.\dfrac{1}{4}=25y^2-9x^2\)
\(\left(\dfrac{3}{4}y-\dfrac{1}{2}x\right)\left(x+\dfrac{3}{2}y\right)=\left(\dfrac{3}{2}y-x\right)\left(\dfrac{3}{2}y+x\right)=\dfrac{9}{4}y^2-x^2\)
\(\left(a+b+c\right)\left(a+b+c\right)=\left(a+b+c\right)^2=a^2+b^2+c^2+2ab+2bc+2ac\)
\(\left(x-y+z\right)\left(x+y-z\right)=x^2-\left(y-z\right)^2=x^2-y^2-z^2+2yz\)
\(a,A=5x^2a-10xya+5y^2a\)
\(=5a\left(x^2-2xy+y^2\right)\)
\(=5a\left(x-y\right)^2\)
Thay x = 124; y=24;a=2 ta có
\(5.2\left(124-24\right)^2=10.100^2=100000\)
\(b,B=2x^2+2y^2-x^2z+z-y^2z-2\)
\(=2\left(x^2+y^2-1\right)-z\left(x^2+y^2-1\right)\)
\(=\left(x^2+y^2-1\right)\left(2-z\right)\)
Thay x = 1 ; y = 1; z= -1 ta có
\(\left(1^2+1^2-1\right)\left(2-\left(-1\right)\right)=\left(1+1-1\right)\left(2+1\right)=1.3=3\)
\(c,C=x^2-y^2+2y-1\)
\(=x^2-\left(y^2-2y+1\right)=x^2-\left(y-1\right)^2=\left(x-y+1\right)\left(x+y-1\right)\)
Thay x = 75; y = 26 ta có
\(\left(75-26+1\right)\left(75+26-1\right)=50.100=5000\)