Question

chung minh ( a+b)² = ( a-b)² + 4ab

b) tinh ( a-b)²⁰¹⁵ biet a+b = 9, ab= 20 va a<b

Answer 1

a) Ta có: \(\left(a+b\right)^2=a^2+2ab+b^2=a^2-2ab+b^2+4ab=\left(a-b\right)^2+4ab^{\left(đpcm\right)}\)

b)Từ kết quá câu a),ta suy ra: \(\left(a-b\right)^2=\left(a+b\right)^2-4ab=9^2-4.20=81-80=1\)

\(\Rightarrow a-b=1\Rightarrow\left(a-b\right)^{2015}=1^{2015}=1\)

Vậy \(\left(a-b\right)^{2015}=1\)

Answer 2

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

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

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

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

b,(a+b)=81

suy ra (a+b)^2=81

(a-b)^2+4ab=81

(a-b)^2=81-4*20

(a-b)^2=81-80

(a-b)^2=1

suy ra (a-b)=1hoac (a-b)=-1

a<b suy ra a-b<0

suy ra a-b=-1

(a-b)^2015=(-1)^2015=-1

Answer 3

 Nhầm cầu b đoạn đầu (a+b)=9nha xin lỗi