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a) \(x^2+y^2=x^2+2xy+y^2-2xy\)
\(=\left(x+y\right)^2-2xy=a^2-2b\)
b) \(x^3+y^3=\left(x+y\right)\left(x^2+xy+y^2\right)\)
\(=a\left(x^2+2xy+y^2-xy\right)\)
\(=a\left[\left(x+y\right)^2-xy\right]=a\left(a^2-b\right)=a^3-ab\)
1/Ta có: \(\left(a+b+c\right)^2=a^2+b^2+c^2+2\left(ab+bc+ca\right)=81\)
\(\Rightarrow M=ab+bc+ca=\frac{\left(81-141\right)}{2}\)
a)\(x+y=a\Rightarrow\left(x+y\right)^2=a^2\)
\(\Rightarrow x^2+2xy+y^2=a^2\Rightarrow x^2+y^2=a^2-2xy\Rightarrow x^2+y^2=a^2-2b\)
Đề a,b bạn ghi mik ko hiểu
c)Ta có : \(x+y=a=>x^2+y^2+2xy=a^2\)
Mà \(x^2+y^2=b\)nên\(b+2xy=a^2=>xy=\frac{a^2-b}{2}\)
\(x^3+y^3=\left(x+y\right)\left(x^2+y^2-xy\right)\)
Thay \(x+y=a\) ; \(x^2+y^2=b\)và \(xy=\frac{a^2-b}{2}\)ta có : \(x^3+y^3=a\left(b-\frac{a^2-b}{2}\right)=ab-\frac{a^3-ab}{2}\)
a, \(A=x^3y\left(x^4-y^3\right)-x^2y\left(x^5-y^3\right)\)
\(=x^7y-x^3y^4-x^7y+x^2y^3\)
\(=-x^3y^4+x^2y^3\)
\(=-x^2y^3\left(xy+1\right)\)
Thay x = -1 ; y = 2 ta có:
\(-\left(-1\right)^2.2^3\left(\left(-1\right).2+1\right)=-1.8\left(-2+1\right)=-8.-1=8\)
b, \(B=x^3y^3\left(x^4-y^4\right)-x^3y^4\left(x^2-y^3\right)\)
\(=x^7y^3-x^3y^7-x^5y^6+x^3y^7\)
\(=x^7y^3-x^5y^6\)
\(=x^5y^3\left(x^2-y^3\right)\)
Thay x=1 ; y =2 ta có :
\(1^5.2^3\left(1^2-2^3\right)=1.8\left(1-8\right)=8.\left(-7\right)=-56\)
\(A=4x^2-2\left(y+2,5x^2\right)+x^2-4y\)
\(=4x^2-2y-5x^2+x^2-4y=-6y\)
\(B=\left(x+y\right).\left(x^4-x^3y+x^2y^2-xy^3+y^4\right)-\left(x^5+y^5-8\right)\)
\(=x^5-x^4y+x^3y^2-x^2y^3+xy^4+x^4y-x^3y^2+x^2y^3-xy^4+y^5-x^5-y^5+8\)
\(=8\)
Vậy BT B ko phụ thuộc vào biến
câu sau tương tự
\(5x\left(x+1\right)-3\left(x-5\right)+4\left(3x-6\right)=2x^2-7\)
\(\Rightarrow5x^2+5x-3x+15+12x-24=2x^2-7\)
\(\Rightarrow5x^2+14x-9=2x^2-7\Rightarrow5x^2+14x-9-2x^2+7=0\)
\(\Rightarrow3x^2+14x-2=0\)
\(\Rightarrow3\left(x^2+\frac{14}{3}x-\frac{2}{3}\right)=0\Rightarrow x^2+2.x.\frac{7}{3}+\frac{49}{9}-\frac{55}{9}=0\)
\(\Rightarrow\left(x+\frac{7}{3}\right)^2=\frac{55}{9}\Rightarrow x+\frac{7}{3}\in\left\{\sqrt{\frac{55}{9}};-\sqrt{\frac{55}{9}}\right\}\Rightarrow x\in\left\{\sqrt{\frac{55}{9}}-\frac{7}{3};-\sqrt{\frac{55}{9}}-\frac{7}{3}\right\}\)
\(a,x^2+y^2=\left(x+y\right)^2-2xy=a^2-2b\)
\(b,x^3+y^3=\left(x+y\right)\left(x^2-xy+y^2\right)\)
\(=\left(x+y\right)\left[\left(x+y\right)^2-2xy-xy\right]\)
\(=\left(x+y\right)\left[\left(x+y\right)^2-3xy\right]\)
\(=a.\left(a^2-3b\right)\)
\(=a^3-3ab\)
câu c bạn ơi