tìm x,y \(\in Z\) biết \(x^2.\left(y-1\right)+y^2.\left(x-1\right)=1\)
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Giúp nha :
Tìm x ; y ; z biết :
\(\sqrt{\left(x+1\right)^2+\left(y+1\right)^2+\left(z+1\right)^2}+3\left(x^2-1\right)\left(y^2-1\right)\left(z^2-1\right)+\left(x-1\right)\left(y-1\right)\left(z-1\right)=0\)
\(Cho\text{ }x,y,z\text{ }\in R\text{ thỏa}\text{ }xyz=1.\text{Tìm Min:}\)
\(P=\left(\left|xy\right|+\left|yz\right|+\left|zx\right|\right)\left[15\sqrt{x^2+y^2+z^2}-7\left(x+y-z\right)\right]+1\)
\(\text{Cho x,y,z }\in R\text{ thỏa mãn điều kiện }xyz=1\text{.Tìm Min:}\)
\(P=\left(\left|xy\right|+\left|yz\right|\left|zx\right|\right).\left[15\sqrt{x^2+y^2+z^2}-7\left(x+y-z\right)\right]+1\)
\(\left|xy\right|+\left|yz\right|+\left|zx\right|\)
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Tìm \(x;y\in Z\)
1)\(x\left(x+1\right)\left(x+7\right)\left(x+8\right)=y^2\)
2)\(y\left(y+1\right)\left(y+2\right)\left(y+3\right)=x^2\)
Xem thêm câu trả lời
ta có : x^2+1x^2+xy+yz+zxxleft(x+yright)+zleft(x+yright)left(x+yright)left(x+zright)Tương tự ta đc y^2+1left(y+xright)left(y+zright) z^2+1left(z+xright)left(z+yright)ĐẶt Axsqrt{frac{left(1+y^2right)left(1+z^2right)}{left(1+x^2right)}}+ysqrt{frac{left(1+z^2right)left(1+x^2right)}{left(1+y^2right)}}+zsqrt{frac{left(1+x^2right)left(1+y^2right)}{left(1+z^2right)}}Rightarrow Axsqrt{frac{left(x+yright)left(y+zright)left(z+xright)left(y+zright)}{left(x+yright)left(x+zright)}}+ysq...
Đọc tiếp
ta có : \(x^2+1=x^2+xy+yz+zx=x\left(x+y\right)+z\left(x+y\right)=\left(x+y\right)\left(x+z\right)\)
Tương tự ta đc \(y^2+1=\left(y+x\right)\left(y+z\right)\)
\(z^2+1=\left(z+x\right)\left(z+y\right)\)
ĐẶt \(A=x\sqrt{\frac{\left(1+y^2\right)\left(1+z^2\right)}{\left(1+x^2\right)}}+y\sqrt{\frac{\left(1+z^2\right)\left(1+x^2\right)}{\left(1+y^2\right)}}+z\sqrt{\frac{\left(1+x^2\right)\left(1+y^2\right)}{\left(1+z^2\right)}}\)
\(\Rightarrow A=x\sqrt{\frac{\left(x+y\right)\left(y+z\right)\left(z+x\right)\left(y+z\right)}{\left(x+y\right)\left(x+z\right)}}+y\sqrt{\frac{\left(z+x\right)\left(z+y\right)\left(x+y\right)\left(x+z\right)}{\left(x+y\right)\left(y+z\right)}}+z\sqrt{\frac{\left(x+y\right)\left(x+z\right)\left(y+z\right)\left(y+x\right)}{\left(z+x\right)\left(z+y\right)}}\)
\(\Rightarrow A=x\left(y+z\right)+y\left(x+z\right)+z\left(x+y\right)=2\left(xy+yz+zx\right)=2\)
\(Tìm\ các\ số\ x,y,z \in Q\ biết \ rằng\)
\(\left(x+y\right):\left(5-z\right):\left(y+z\right):\left(9+y\right)=3:1:2:5\)
Bài 1 :
a) \(16.\left(38-2\right)-38\left(16-1\right)\)
b) \(\left(-41\right).\left(59+2\right)+59\left(41-2\right)\)
Bài 2 :
Tìm các số x ; y ; x biết rằng :
\(\)x + y = 2 ; y + z = 3 ; z + x = -5
Bài 3 : Tìm x ; y \(\in\) Z biết rằng :
( y + 1 ) . xy - 1 ) = 3
Bài 1 : Tính nhanh
a) 16.(38−2)−38(16−1)16.(38−2)−38(16−1)
b) (−41).(59+2)+59(41−2)(−41).(59+2)+59(41−2)
Bài 2 :
Tìm các số x ; y ; x biết rằng :
x + y = 2 ; y + z = 3 ; z + x = -5
Bài 3 : Tìm x ; y ∈∈ Z biết rằng :
( y + 1 ) . xy - 1 ) = 3
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a) 16.(38−2)−38(16−1)
= 16.38 - 16.2 - 38.16 - 38.1
=-16.2 - 38.1
=-32-38
=-70
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Cho x, y, z đôi một khác nhau thỏa mãn \(\left(x+z\right)\left(y+z\right)=1\). Tìm Min
\(M=\dfrac{1}{\left(x-y\right)^2}+\dfrac{1}{\left(x+z\right)^2}+\dfrac{1}{\left(y+z\right)^2}\)
Cho x,y,z>0 thỏa mãn: x+y+z=3. Tìm GTNN của \(P=\frac{\left(x+1\right)^2.\left(y+1\right)^2}{z^2+1}+\frac{\left(y+1\right)^2.\left(z+1\right)^2}{x^2+1}+\frac{\left(z+1\right)^2.\left(x+1\right)^2}{y^2+1}\)