Question

Cm : \(\left(a-b\right)^2=\left(a+b\right)^2-4ab\)

Tính \(\left(a-b\right)^{2017}\) biết \(a+b=7\) và \(ab=12\)

Answer 1

a) Ta có:\(VT=a^2-2ab+b^2\)

\(=a^2+2ab+b^2-4ab=\left(a+b\right)^2-4ab=VP\)

Vậy ...

b) \(a+b=7\Rightarrow\left(a+b\right)^2=7^2=49\)

\(\Leftrightarrow a^2+2ab+b^2=49\)

\(\Leftrightarrow a^2+24+b^2=49\)

\(\Leftrightarrow a^2+b^2=25\)

\(\Leftrightarrow\left(a-b\right)^2+2ab=25\)

\(\Leftrightarrow\left(a-b\right)^2=25-24=1\)

\(\Leftrightarrow\left[{}\begin{matrix}a-b=1\\a-b=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left(a-b\right)^{2017}=1\\\left(a-b\right)^{2017}=-1\end{matrix}\right.\)

Vậy (a - b)²⁰¹⁷ = 1 hoặc (a - b)²⁰¹⁷ = -1.

Answer 2

Câu 1:

Ta có:

\(VP=\left(a+b\right)^2-4ab=a^2+2ab+2b^2-4ab\)

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

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

Chúc bạn học tốt!!!

Answer 3

(a-b)²⁰¹⁷ ??????

Answer 4

Sửa đề : Tính \(\left(a-b\right)^2\) biết \(a+b=7\) và \(ab=12\)

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

\(\Rightarrow\left(a-b\right)^2=7^2-4.12\)

\(=1\)