作业帮谁能教我一道高中数学题
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谁能教我一道高中数学题
设x=x1 x=x2 是方程组 y平方=4x 的两组解,且|y1-y2|=8.求K的值
y=y1 y=y2 y=k(x-1)
设x=x1 x=x2 是方程组 y平方=4x 的两组解,且|y1-y2|=8.求K的值
y=y1 y=y2 y=k(x-1)
解决思路是先解方程组 Y^2=4X ==> K^2(X-1)^2=4X
Y=K(X-1)
==> K^2X^2-(2K^2+4)X+K^2 =0 ==> X1+X2=-(-(2K^2+4))/K^2=2+4/K^2
X1X2 =K^2/K^2 =1
Y1=K(X1-1) ==> Y1-Y2=K(X1-X2)
Y2=K(X2-1)
|Y1-Y2|=|K(X1-X2)|
K^2(X1-X2)^2=K^2(X1^2-2X1X2+X2^2)=K^2(X1+X2)^2-4K^2X1X2
代入上面求的X1X2,X1+X2
|K(X1-X2)|^2=K^2(X1-X2)^2=8^2=64
K^2(2+4/K^2)^2-4K^2*1=4K^2+16+16/K^2-4K^2=16+16K^2=64
K=根号3/3或K=-根号3/3
Y=K(X-1)
==> K^2X^2-(2K^2+4)X+K^2 =0 ==> X1+X2=-(-(2K^2+4))/K^2=2+4/K^2
X1X2 =K^2/K^2 =1
Y1=K(X1-1) ==> Y1-Y2=K(X1-X2)
Y2=K(X2-1)
|Y1-Y2|=|K(X1-X2)|
K^2(X1-X2)^2=K^2(X1^2-2X1X2+X2^2)=K^2(X1+X2)^2-4K^2X1X2
代入上面求的X1X2,X1+X2
|K(X1-X2)|^2=K^2(X1-X2)^2=8^2=64
K^2(2+4/K^2)^2-4K^2*1=4K^2+16+16/K^2-4K^2=16+16K^2=64
K=根号3/3或K=-根号3/3