Từ \(\hept{\begin{cases}2x=3y< =>\frac{x}{3}=\frac{y}{2}\\4z=5x< =>\frac{z}{5}=\frac{x}{4}\end{cases}< =>\frac{x}{12}}=\frac{y}{8}=\frac{z}{15}\)

Đặt \(\frac{x}{12}=\frac{y}{8}=\frac{z}{15}=k\)

\(< =>\hept{\begin{cases}\frac{x}{12}=k< =>x=12k\\\frac{y}{8}=k< =>y=8k\\\frac{z}{15}=k< =>z=15k\end{cases}}\)

Khi đó \(3y^2-z^2=-33\)

\(< =>z^2-3y^2=33\)

\(< =>\left(15k\right)^2-3\left(8k\right)^2=33\)

\(< =>225k^2-3.64k^2=33\)

\(< =>225k^2-192k^2=33\)

\(< =>33k^2=33\)

\(< =>k^2=1< =>\orbr{\begin{cases}k=1\left(1\right)\\k=-1\left(2\right)\end{cases}}\)

Với \(\left(1\right)< =>\hept{\begin{cases}x=12k=12\\y=8k=8\\z=15k=15\end{cases}}\)

Với \(\left(2\right)< =>\hept{\begin{cases}x=12k=-12\\y=8k=-8\\z=15k=-15\end{cases}}\)

Vậy ta có 2 bộ số \(\left\{x;y;z\right\}=\left\{-12;-8;-15\right\};\left\{12;8;15\right\}\)

làm kiểu j` vậy

\(A=4x^2+12xy+9y^2\)

\(B=25x^2-10xy+y^2\)

\(C=8x^3+12x^2y^2+6xy^4+y^6\)

\(D=\left(x^2\right)^2-\left(\dfrac{2}{5}y\right)^2=x^4-\dfrac{4y^2}{25}\)

\(E=x^3-27y^3\)

\(F=x^6-27\)

\(a,A+B-C=16x^4-8x^3y+7x^2y^2-9y^4-15x^4+3x^3y-5x^2y^2-6y^4-5x^3y-3x^2y^2-17y^4-1\)

\(=\left(16x^4-15x^4\right)+\left(-8x^3y+3x^3y-5x^3y\right)+\left(7x^2y^2-5x^2y^2-3x^2y^2\right)+\left(-9y^4-6y^4-17y^4\right)-1\)

\(=x^4-10x^3y-x^2y^2-32y^4-1\)

\(b,A-C+B=A+B-C\) ( giống câu a )

\(a,\)

\(A+B+C\)

\(=16x^4-8x^3y+7x^2y^2-9y^4-15x^4+3x^3y-5x^2y^2-6y^4-\left(5x^3y+3x^2y^2+17y^4+1\right)\)

\(=16x^4-8x^3y+7x^2y^2-9y^4-15x^4+3x^3y-5x^2y^2-6y^4-5x^3y-3x^2y^2-17y^4-1\)

\(=\left(16x^4-15x^4\right)+\left(-9y^4-6y^4-17y^4\right)+\left(-8x^3y+3x^3y-5x^3y\right)+\left(7x^2y^2-5x^2y^2-3x^2y^2\right)-1\)

\(=x^4-32y^4-10x^3y-x^2y^2-1\)

\(b,\)

\(A-C+B=A+B-C=x^4-32y^4-10x^3y-x^2y^2-1\)

a: A+B-C

=16x^4-8x^3y+7x^2y^2-9y^4-15x^4+3x^3y-5x^2y^2-6y^4-C

=x^4-5x^3y+2x^2y^2-15y^4-5x^3y-3x^2y^2-17y^4-1

=x^4-10x^3y-x^2y^2-32y^4-1

b: A-C+B=A+B-C=x^4-10x^3y-x^2y^2-32y^4-1

ta có: \(\frac{1+3y}{12}=\frac{1+6y}{2x}=\frac{1+9y}{5x}\)

\(\Rightarrow\frac{1+3y}{12}=\frac{1+6y}{2x}=\frac{1+6y-1-3y}{2x-12}=\frac{3y}{2x-12}\)

\(\Rightarrow\frac{3y}{2x-12}=\frac{1+9y}{5x}=\frac{9y+1-3y}{5x-2x+12}=\frac{1+6y}{3x+12}\)

\(\Rightarrow\frac{1+6y}{3x+12}=\frac{1+6y}{2x}\)

=> 3x + 12 = 2x 

=> 3x - 2x = - 12

x = -12

xog r bn chỉ cần thay x = -12 vào 2 trong 3 p/s bất kì trên là tính đk y

\(\frac{1+3y}{12}=\frac{1+6y}{2x}=\frac{1+9y}{5x}=\frac{1+3y+1+9y}{12+5x}=\frac{2+12y}{12+5x}\)

\(\Rightarrow\frac{1+6y}{2x}=\frac{2+12y}{12+5x}\)

\(\Rightarrow\frac{12+5x}{2}=2x\)

\(\Rightarrow12+5x=4x\)

\(\Rightarrow12=-x\Leftrightarrow x=-12\)

Thay x vô mà tìm y

1+6y/2x=1+9y/5x=1+3y/12

=>1+6y/2=1+9y/5=1+3y/12 (nhân cả 2 vế với x)

=>12*(1+6y)=2*(1+3y)

=>12+72y=2+6y

=>72y-6y=2-12

=>66y=-10

=>y=-10/66

=>y=-5/33

RỒI BẠN TỰ THAY Y VÀO ĐỂ TIM X

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