Question

 

x²-2x+y²+4y+5=0

32)CMR nếu: (a + b + c +d)(a - b - c + d)=(a - b +c - d)(a + b -c - d)thì \(\dfrac{a}{c}=\dfrac{b}{d}\)(a,b,c,d khác 0)

 

Answer 1

Câu 1:

\(\Leftrightarrow x^2-2x+1+y^2+4y+4=0\)

\(\Leftrightarrow\left(x-1\right)^2+\left(y+2\right)^2=0\)

=>x=1 và y=-2

Answer 2

Câu 2:

Áp dụng tính chất của DTSBN, ta có \(\left(a+b+c+d\right)\left(a-b-c+d\right)=\left(a-b+c-d\right)\left(a+b-c-d\right)\Leftrightarrow\dfrac{a+b+c+d}{a+b-c-d}=\dfrac{a-b+c-d}{a-b-c+d}=\dfrac{a+c}{a-c}\)Khi đó, ta có \(\left(a-c\right)\left(a+b+c+d\right)=\left(a+c\right)\left(a+b-c-d\right)\Leftrightarrow a^2-ca+ab-bc+ac-c^2+ad-cd=a^2+ca+ab+bc-ca-c^2-ad-dc-bc+ac\Leftrightarrow2ad=2bc\Leftrightarrow ad=bc\Leftrightarrow\dfrac{a}{c}=\dfrac{b}{d}\left(đpcm\right)\)