Gọi d là ước của 9n+2 và 12n+3 nên

\(9n+2⋮d\Rightarrow4\left(9n+2\right)=36n+8⋮d\)

\(12n+3⋮d\Rightarrow3\left(12n+3\right)=36n+9⋮d\)

\(\Rightarrow36n+9-\left(36n+9\right)=1⋮d\Rightarrow d=1\)

=> 9n+2 và 12n+3 là 2 số nguyên tố cùng nhau

Gọi d là ƯC(9n + 2; 12n + 3)

⇒ 9n + 2 ⋮ d ⇒ 36n + 8 ⋮ d

12n + 3 ⋮ d ⇒ 36n + 9 ⋮ d

⇒ (36n + 9) - (36n - 8) ⋮ d

⇒ 1 ⋮ d

⇒ d = 1

Vậy 9n + 2 và 12n + 3 là hai số nguyên tố cùng nhau

\(\left(x^2-x+1\right)^2=x^4+x^2+1-2x^3+2x^2-2x=x^4-2x^3+3x^2-2x+1\)

Vậy a = -2; b = 1.

G

Ta có :

\(\left(a+b+c\right)=0\)

\(\Leftrightarrow\left(a+b+c\right)^2=0\)

\(\Leftrightarrow a^2+b^2+c^2+2\left(ab+bc+ca\right)=0\)

\(\Leftrightarrow a^2+b^2+c^2=-2\left(ab+bc+ca\right)\)

\(\Leftrightarrow\left(a^2+b^2+c^2\right)^2=\left[-2\left(ab+bc+ca\right)\right]^2\)

\(\Leftrightarrow a^4+b^4+c^4+2\left(a^2b^2+b^2c^2+c^2a^2\right)=4\left(a^2b^2+b^2c^2+c^2a^2+2a^2bc+2ab^2c+2abc^2\right)\left(1\right)\)

\(\Leftrightarrow a^4+b^4+c^4=4\left(a^2b^2+b^2c^2+c^2a^2+2abc\left(a+b+c\right)\right)-2\left(a^2b^2+b^2c^2+c^2a^2\right)\)

\(\Leftrightarrow a^4+b^4+c^4=2\left(a^2b^2+b^2c^2+c^2a^2\right)\left(2\right)\) (vì \(a+b+c=0\))

\(\left(1\right)+\left(2\right)\Rightarrow2\left(a^4+b^4+c^4\right)=4\left(a^2b^2+b^2c^2+c^2a^2+2a^2bc+2ab^2c+2abc^2\right)\)

\(\Rightarrow\left(a^4+b^4+c^4\right)=2\left(ab+bc+ca\right)^2\)

\(\Rightarrow dpcm\)

\(\dfrac{x}{15}\)+\(\dfrac{x}{12}\)=4/1+1/2=9/2

=>x(\(\dfrac{1}{15}\)+\(\dfrac{1}{12}\))=9/2

=>x\(\cdot\)\(\dfrac{3}{20}\)=9/2

=>x=9/2:3/20=30

Vậy x=30

\(\dfrac{x}{15}+\dfrac{x}{12}=\dfrac{9}{2}\Rightarrow\left(\dfrac{1}{15}+\dfrac{1}{12}\right)x=\dfrac{9}{2}\)

\(\Rightarrow\left(\dfrac{12+18}{180}\right)x=\dfrac{9}{2}\Rightarrow\dfrac{30}{180}x=\dfrac{9}{2}\Rightarrow\dfrac{1}{6}x=\dfrac{9}{2}\Rightarrow x=\dfrac{9}{2}.6=27\)

đề kiểu j thế???

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