Question

C1: Chứng minh: (a+b)² - (a-b)² = 4ab

C2: Tìm x biết: (2x+3)² - 4(x-1).(x+1) = 49

Answer 1

C1: \(\left(a+b\right)^2-\left(a-b\right)^2\)

\(=a^2+2ab+b^2-a^2+2ab-b^2=4ab\) (đpcm)

C2: \(\left(2x+3\right)^2-4\left(x-1\right)\left(x+1\right)=49\)

\(\Leftrightarrow4x^2+12x+9-4x^2+4=49\)

\(\Leftrightarrow12x+13=49\)

\(\Leftrightarrow12x=36\)

\(\Leftrightarrow x=3\)

Vậy x = 3.

Answer 2

Câu 1 :

\(\left(a+b\right)^2-\left(a-b\right)^2\)

= \(\left(a^2+2ab+b^2\right)-\left(a^2-2ab+b^2\right)\)

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

= \(\left(a^2-a^2\right)+\left(2ab+2ab\right)+\left(b^2-b^2\right)\)

= \(4ab\)

Vậy................(đpcm)