9+1465+1

\(x+y+z=0\)

\(\Rightarrow\left(x+y+z\right)^2=0\)

\(\Rightarrow x^2+y^2+z^2+2.\left(xy+yz+xz\right)=0\)

\(\Rightarrow1+2.\left(xy+yz+xz\right)=0\)

\(\Rightarrow xy+yz+xz=\frac{-1}{2}\)

\(\Rightarrow\left(xy+yz+xz\right)^2=\frac{1}{4}\)

\(\Rightarrow x^2y^2+y^2z^2+x^2z^2+2.\left(xy^2z+xyz^2+x^2yz\right)=\frac{1}{4}\)

\(\Rightarrow x^2y^2+y^2z^2+x^2z^2=\frac{1}{4}\)

\(x^2+y^2+z^2=1\)

\(\Rightarrow\left(x^2+y^2+z^2\right)^2=1\)

\(\Rightarrow x^4+y^4+z^4+2.\left(x^2y^2+y^2z^2+x^2z^2\right)=1\)

\(\Rightarrow x^4+y^4+z^4+2.\frac{1}{4}=1\)

\(\Rightarrow x^4+y^4+z^4=\frac{1}{2}\)

\(\Rightarrow S=\frac{1}{2}\)

a, b là 2 số tự nhiên liên tiếp nên b=a+1. Thay vào p ta có:

p = a²+(a+1)²+a²*(a+1)²

p= a²+a²+2a+1+a²(a²+2a+1)

p=a⁴+ 2a³+3a²+2a+1

p=(a⁴+2a³+a) +2 (a²+a) +1

p=(a²+a)²+2 (a²+a) +1

p=[(a²+a) + 1]²

Vậy p là số chính phương.

Nếu a lẻ thì (a²+a) chẵn => p lẻ

Nếu a chẵn thì (a²+a) chẵn => p lẻ

Vậy p là số chính phương lẻ.

1)2xy−2y²+3x−3y1)2xy−2y²+3x−3y

=2y(x−y)+3(x−y)=2y(x−y)+3(x−y)
=(2y+3)(x−y)=(2y+3)(x−y)

2)x²−9y²+x+3y2)x²−9y²+x+3y

=x²−(3y)²+(x+3y)=x²−(3y)²+(x+3y)

=(x−3y)(x+3y)+(x+3y)=(x−3y)(x+3y)+(x+3y)

=(x−3y+1)(x+3y)=(x−3y+1)(x+3y)
3)3x(2x−3)−6x+93)3x(2x−3)−6x+9
=3x(2x−3)−3(2x−3)=3x(2x−3)−3(2x−3)
=(3x−3)(2x−3)=(3x−3)(2x−3)
=3(x−1)(2x−3)=3(x−1)(2x−3)

4)y²−25−x²−10x4)y²−25−x²−10x
=−(x²+10x+25)+y²=−(x²+10x+25)+y²
=−(x+5)²+y²=−(x+5)²+y²

=y²−(x+5)²=y²−(x+5)²
=(y−x−5)(y+x+5)=(y−x−5)(y+x+5)
5)x²−10x+245)x²−10x+24

=x²−4x−6x+24=x²−4x−6x+24
=x(x−4)−6(x−4)=x(x−4)−6(x−4)
=(x−6)(x−4)

18𝑥2−24𝑥+8−9𝑥2+4=0

18x^{2}-24x+{\color{#c92786}{8}}-9x^{2}+{\color{#c92786}{4}}=018x2−24x+8−9x2+4=0

18𝑥2−24𝑥+12−9𝑥2=0

𝑥=2𝑥=2/3

2(3x - 2)² - 9x² + 4 = 0

<=> 2(9x² - 12x + 4) - 9x² + 4 = 0

<=> 9x² - 24x + 12 = 0

<=> 9x² - 18x - 6x + 12  = 0

<=> 9x(x - 2) - 6(x - 2) = 0

<=> (9x - 6)(x - 2) = 0 

<=> \(\orbr{\begin{cases}x-2=0\\9x-6=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=2\\x=\frac{2}{3}\end{cases}}\)

TL

x=2/3

x=2

2(3𝑥−2)2−9𝑥2+4=0

2\left(3x-2\right)^{2}-9x^{2}+4=02(3x−2)2−9x2+4=0

2(3𝑥−2)(3𝑥−2)−9𝑥2+4=0

2(3𝑥−2)(3𝑥−2)−9𝑥2+4=0

2{\color{#c92786}{(3x-2)(3x-2)}}-9x^{2}+4=02(3x−2)(3x−2)−9x2+4=0

2(3𝑥(3𝑥−2)−2(3𝑥−2))−9𝑥2+4=0

x = 2 

x = 2/3