\(\frac{ay-bx}{c}=\frac{cx-az}{b}=\frac{bz-cy}{a}\)

\(\Rightarrow\frac{acy-bcx}{c^2}=\frac{bcx-abz}{b^2}=\frac{abz-acy}{a^2}=\frac{0}{a^2+b^2+c^2}=0\)

\(\Rightarrow\hept{\begin{cases}ay-bx=0\\cx-az=0\\bz-cy=0\end{cases}}\)

\(\Rightarrow\left(ay-bx\right)^2+\left(cx-az\right)^2+\left(bz-ay\right)^2=0\)

\(\Rightarrow a^2y^2-2axby+b^2x^2+a^2z^2-2axcz+c^2x^2+b^2z^2-2bycz\)

\(+c^2y^2=0\)

\(\Rightarrow a^2x^2+a^2y^2+a^2z^2+b^2x^2+b^2y^2+b^2z^2+c^2x^2+c^2y^2+c^2z^2\)

\(=a^2x^2+b^2y^2+c^2z^2+2axby+2bycz+2axcz\)

\(\Rightarrow\left(x^2+y^2+z^2\right)\left(a^2+b^2+c^2\right)=\left(ax+by+cz\right)^2\)

#)Giải :

Ta có : \(\hept{\begin{cases}ax+by=c\\bx+cy=a\\cx+ay=b\end{cases}\Rightarrow ax+by+bx+cy+cx+ay=c+a+b}\)

\(\Rightarrow x\left(a+b+c\right)+y\left(a+c+b\right)=a+b+c\)

\(\Rightarrow\left(x+y-1\right)\left(a+b+c\right)=0\)

\(\Rightarrow a+b+c=0\Rightarrow a+b=-c\)

\(\Rightarrow a^3+b^3+c^3=a^3+3ab\left(a+b\right)+b^3-3ab\left(a+b\right)+c^3\)

\(=\left(a+b\right)^3-3ab\left(a+b\right)+c^3\)

\(=\left(-c\right)^3-3ab\left(-c\right)+c^3=3abc\)

\(\Rightarrowđpcm\)

Bài giải thiếu trường hợp \(x+y-1=0\) rồi

-3(a+b+c)(a^2-2ab+b^2-2ac-2bc+c^2)

a) 2³⁰ = ( 2² )¹⁵ = 4¹⁵  < 22¹⁵ . 3¹⁵

b) 3²⁰ = ( 3⁴ )⁵ = 81⁵ 

2²⁰ . 5⁵ = ( 2⁴ )⁵ . 5⁵ = ( 2⁴ . 5 )⁵ = 80⁵

nên 3²⁰ < 2²⁰ . 5⁵

https://olm.vn/hoi-dap/detail/108858274535.html

Bài tương tự gưi link ib

\(\hept{\begin{cases}\left(x+2y\right)\left(x^2-2xy+4y^2\right)=0\\\left(x-2y\right)\left(x^2+2xy+4y^2\right)=16\end{cases}}\)

<=> \(\hept{\begin{cases}x^3+8y^3=0\left(1\right)\\x^3-8y^3=16\left(2\right)\end{cases}}\)

Lấy (1) + (2) theo vế

=> 2x³ = 16

=> x³ = 8 = 2³

=> x = 2

Thế x = 2 vào (1)

=> 2³ + 8y³ = 0

=> 8 + 8y³ = 0

=> 8y³ = -8

=> y³ = -1 = (-1)³

=> y = -1

Vậy \(\hept{\begin{cases}x=2\\y=-1\end{cases}}\)

a) Vì \(x-y=1\)

\(\Rightarrow\left(x-y\right)^3=1\)

\(\Leftrightarrow x^3-y^3-3xy\left(x-y\right)=1\)

\(\Leftrightarrow x^3-y^3-3xy=1\)

b) \(B=2\left(x^3-y^3\right)-3\left(x+y\right)^2\)

\(=2\left(x-y\right)\left(x^2+xy+y^2\right)-3\left(x^2+2xy+y^2\right)\)

\(=4\left(x^2+xy+y^2\right)-3\left(x^2+2xy+y^2\right)\)

\(=4x^2+4xy+4y^2-3x^2-6xy-3y^2\)

\(=x^2-2xy+y^2\)

\(=\left(x-y\right)^2\)

\(=4\)

a,

\(x^2+5x+6=x^2+2x+3x+6=x\left(x+2\right)+3\left(x+2\right)=\left(x+2\right)\left(x+3\right)\)

b,

\(3x^2-7x+2=3x^2-x-6x+2=x\left(3x-1\right)-2\left(3x-1\right)=\left(3x-1\right)\left(x-2\right)\)

c,

\(a^3+b^3+c^3-3abc=\left(a+b\right)^3-3ab\left(a+b+c\right)+c^3\)

\(=\left(a+b+c\right)\left(\left(a+b\right)^2-\left(a+b\right)c+c^2\right)-3ab\left(a+b+c\right)\)

=)

a) \(x^2+5x+6\)

\(=x^2+2x+3x+6\)

\(=x\left(x+2\right)+3\left(x+2\right)\)

\(=\left(x+3\right)\left(x+2\right)\)

b) \(3x^2-7x+2\)

\(=3x^2-x-6x+2\)

\(=x\left(3x-1\right)-2\left(3x-1\right)\)

\(=\left(x-2\right)\left(3x-1\right)\)

c) Phân tích thành nhân tử $a^3 + b^3 + c^3 - 3abc$ - Đại số - Diễn đàn Toán học

Phân tích  đa thức thành nhân tử nha các bn

up tut làm quen luôn phân tích cái j :3