Giup minh giai cau nay voi: ( Chi nhung ai gioi Toan lop 7 tro len moi giai duoc)Cau 1: Cho \(\frac{1}{c}\) = \(\frac{1}{2}\) (\(\frac{1}{a}+\frac{1}{b}\) ) ( voi a, b, c khac 0 ; b khac c )C/m rang \(\frac{a}{b}=\frac{a-c}{c-b}\) Cau 2: Tim cac gia tri cua x,y thoa man...
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Giup minh giai cau nay voi: ( Chi nhung ai gioi Toan lop 7 tro len moi giai duoc)
Cau 1: Cho \(\frac{1}{c}\) = \(\frac{1}{2}\) (\(\frac{1}{a}+\frac{1}{b}\) ) ( voi a, b, c khac 0 ; b khac c )
C/m rang \(\frac{a}{b}=\frac{a-c}{c-b}\)
Cau 2: Tim cac gia tri cua x,y thoa man :
\(|2x-27|^{2011}+\left(3y+10\right)^{2012}=0\)
\(\frac{1}{c}=\frac{1}{2}.\left(\frac{1}{a}+\frac{1}{b}\right)\Rightarrow\frac{1}{c}=\frac{a+b}{2ab}\Rightarrow c=\frac{2ab}{a+b}\)
\(\frac{a-c}{c-b}=\frac{a-\frac{2ab}{a+b}}{\frac{2ab}{a+b}-b}=\frac{\frac{a^2+ab-2ab}{a+b}}{\frac{2ab-ab-b^2}{a+b}}=\frac{a^2+ab-2ab}{2ab-ab-b^2}=\frac{a.\left(a-b\right)}{b.\left(a-b\right)}=\frac{a}{b}\)(ĐPCM)
\(\left|2x-27\right|^{2017}+\left(3y+10\right)^{2012}\Rightarrow\hept{\begin{cases}2x-27=0\\3y+10=0\end{cases}}\Rightarrow\hept{\begin{cases}x=\frac{27}{2}\\y=-\frac{10}{3}\end{cases}}\)(làm tắt nha, có gì bn thêm vào)
câu 2 : | 2x - 27 |\(^{2011}\)+ ( 3y + 10 ) \(^{2012}\)=0
=> \(\left|2x-27\right|^{2011}\)lớn hơn hoặc = 0 (1)
=> \(\left(3y+10\right)^{2012}\)>hoặc = 0(2)
mà (1) + (2) =0
nên => \(\left|2x-27\right|^{2011}=0\)và \(\left(3y+10\right)^{2012}=0\)
\(\left|2x-27\right|^{2011}=0^{2011}\) \(\left(3y+10\right)^{2012}=0^{2012}\)
\(\left|2x-27\right|=0\) 3y + 10 = 0
2x = 27 3y = -10
x = 27 : 2 y = -10 : 3
x = 13,5 y = \(\frac{-10}{3}\)