Question

Cho ( a+b)² = 2(a²+b²). CM: a= b

Answer 1

( a + b)² = 2(a² + b²)

=> a² + 2ab + b² = 2a² + 2b²

=> a² + 2ab + b² - 2a² - 2b² = 0

=> (-a)² + 2ab + (-b)² = 0

=> - ( a² - 2ab + b² ) = 0

=> - ( a - b )² = 0²

=> - a + b = 0

=> b = 0 - ( - a )

=> b = a

Vậy a = b khi ( a + b )² = 2(a² + b²)

Answer 2

(a+b)^2=2(a^2+b^2)

a^2+2ab+b^2-2a^2-2b^2=0

-a^2-b^2+2ab=0

-(a^2-2ab+b^2)=0

-(a-b)^2=0

(a-b)^2=0

a-b=0

a=b(đpcm)