Question

cho 2 so a,b thoa man : 8.(a² +b²) =(2a + 2b)²

chung minh rang : a= b .

giup minh bai nay nua nha cac ban ^^

Answer 1

Có: \(8\left(a^2+b^2\right)=\left(2a+2b\right)^2\)

\(\Leftrightarrow8a^2+8b^2=4a^2+8ab+4b^2\)

\(\Leftrightarrow4a^2-8ab+4b^2=0\)

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

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

\(\Leftrightarrow a-b=0\Leftrightarrow a=b\)

=> đpcm

Answer 2

8(a²+b²) = (2a + 2b)²

=>8a²+8b²= 4a² + 8ab + 4b

=> 4a² + 4b² = 8ab

=> 4a² + 4b² - 8ab = 0

=> (2a - 2b)² =0

=> 2a - 2b = 0

=> 2(a-b)=0

=>a-b=0

=> a=b