Question

Chứng minh các hệ thức sau : 
1. (a+b)²+(a-b)² = 2(a²+b²)

2. (a+b)² - (a-b)² = 4ab

3.(a+b+c)² + (b+c-a)² + (c+a+-b)² + (a+b-c)²  = 4(a²+b²+c²)

Answer 1

1; (a + b)² + (a - b)² = 2.(a² + b²)

    a² + 2ab + b² + a² - 2ab + b² 

= (a² + a²) + (b² + b²)  +(2ab - 2ab)

= 2a² + 2b² + 0

= 2.(a² + b²) (đpcm)

 

   

Answer 2

1.\(VT=a^2+2ab+b^2+a^2-2ab+b^2\)
          \(=2a^2+2b^2\)
          \(=2.\left(a^2+b^2\right)\left(dpcm\right)\)
2. \(VT=a^2+2ab+b^2-\left(a^2-2ab+b^2\right)\)
          \(=a^2+2ab+b^2-a^2+2ab-b^2\)
          \(=4ab\left(dpcm\right)\)
3.\(VT=\left(a^2+b^2+c^2+2ab+2bc+2ac\right)+\left(b^2+c^2+a^2+2bc-2ab-2ac\right)+\left(c^2+a^2+b^2+2ac-2bc-2ab\right)+\left(a^2+b^2+c^2+2ab-2bc-2ac\right)\)      \(=4a^2+4b^2+4c^2\)
      \(=4.\left(a^2+b^2+c^2\right)\left(dpcm\right)\)

Answer 3

2; CM: (a + b)² - (a - b)² = 4ab

   (a + b)² - (a - b)²

= a² + 2ab + b² - (a² - 2ab + b²)

= a² + 2ab + b² - a² + 2ab - b²

= (2ab + 2ab) + (a² - a²) + (b² - b²)

= 4ab + 0 + 0

= 4ab (đpcm)

Answer 4

1) \(Vế.trái=a^2+2ab+b^2+a^2-2ab+b^2=2a^2+2b^2=2\left(a^2+b^2\right)=vê.phải\)

\(\Rightarrowđpcm\)

2) \(Vế.trái=a^2+2ab+b^2-a^2+2ab-b^2=4ab=vế.phải\)

\(\Rightarrowđpcm\)

Answer 5

@ Rái cá máu lửa lần sau em không nên bỏ bước em nhé!