Ta có: \(x^2=y^2+z^2\)

\(\Leftrightarrow x^2-y^2=z^2\)

\(\Leftrightarrow25\left(x-y\right)\left(x+y\right)=25z^2\)

\(\Leftrightarrow\left(25x-25y\right)\left(x+y\right)=25z^2\)

\(\Leftrightarrow\left(13x-12y+12x-13y\right)\left(13x-12y-12x+13y\right)=25z^2\)

\(\Leftrightarrow\left(13x-12y\right)^2-\left(12x-13y\right)^2=25z^2\)

\(\Leftrightarrow\left(13x-12y\right)^2-\left(5z\right)^2=\left(12x-13y\right)^2\)

\(\Leftrightarrow\left(13x-12y-5z\right)\left(13x-12y+5z\right)=\left(12x-13y\right)^2\)(ĐPCM).

nhanh nào ai trả lời mình cho 3 ****

`12x<sup>2</sup> + 5x – 12y<sup>2</sup> + 12y – 10xy – 3`

`= 12x<sup>2</sup> + 9x – 4x – 12y<sup>2</sup> – 18xy + 8xy  – 3 + 6y – 6y`

`= (12x<sup>2</sup> – 18xy + 9x) – (4x – 6y + 3) + (8xy – 12y<sup>2</sup> + 6y)`

`= 3x(4x – 6y + 3) – (4x – 6y + 3) + 2y(4x – 6y + 3)`

`= (4x – 6y + 3)(3x + 2y – 1).`

$12x² + 5x – 12y² + 12y – 10xy – 3$

$= 12x² + 9x – 4x – 12y² – 18xy + 8xy  – 3 + 6y – 6y$

$= (12x² – 18xy + 9x) – (4x – 6y + 3) + (8xy – 12y² + 6y)$

$= 3x(4x – 6y + 3) – (4x – 6y + 3) + 2y(4x – 6y + 3)$

$= (4x – 6y + 3)(3x + 2y – 1).$

b) Ta có: \(B=5x\left(x-4y\right)-4y\left(y-5x\right)\)

\(=5x^2-20xy-4y^2+20xy\)

\(=5x^2-4y^2\)

\(=5\cdot\left(-\dfrac{1}{5}\right)^2-4\cdot\left(-\dfrac{1}{2}\right)^2\)

\(=5\cdot\dfrac{1}{25}-4\cdot\dfrac{1}{4}\)

\(=\dfrac{1}{5}-1=\dfrac{-4}{5}\)

12x² + 5x - 12y² + 12y - 10xy - 3 

= -(12x² + 10xy + 3 -12x² - 5x - 12y)

Có

12y² + 10xy + 3 - 12x² - 5x - 12y

= 18xy + 12y² - 6y - 12x² - 8xy + 4x - 9x - 6y + 3

= 6y (3x + 2y - 1) - 4 . x (3x + 2y - 1) - 3 . (3x + 2y - 1) 

= (6y - 4x - 3) . (3x + 2y - 1)

a. Ta có: 11a + 14b

           = 110 + a + 140 + b

           = 110 + 140 + a + b

           =  250 + a + b

          =   50 . 5 + a + b chia hết cho 5

b. Ta có: 14a + 26b 

              = 140 + a + 260 + b

              = 140 + 260 + a +b

              = 500 + a + b

              = 5 . 100 + a + b chia hết cho 5

Chúc bn hk tốt nhé !!

a) chứng minh 11a +14b chia hết cho 5

\(11a+14b=110+a+140+b\)

Mà   \(110⋮5\)

         \(140⋮5\)

\(\Rightarrow11a+14b⋮5\)

b)chúng minh 14a + 26b chia hết cho 5

\(14a+26b=140+a+260+b\)

Mà :  \(140⋮5\)

          \(260⋮5\)

\(\Rightarrow14a+26b⋮5\)

Học tốt