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)
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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)](/uploads/image/z/8984737-1-7.jpg?t=%E8%B0%81%E8%83%BD%E6%95%99%E6%88%91%E4%B8%80%E9%81%93%E9%AB%98%E4%B8%AD%E6%95%B0%E5%AD%A6%E9%A2%98%E8%AE%BEx%3Dx1+x%3Dx2+%E6%98%AF%E6%96%B9%E7%A8%8B%E7%BB%84+y%E5%B9%B3%E6%96%B9%3D4x+%E7%9A%84%E4%B8%A4%E7%BB%84%E8%A7%A3%2C%E4%B8%94%7Cy1-y2%7C%3D8.%E6%B1%82K%E7%9A%84%E5%80%BCy%3Dy1+y%3Dy2+y%3Dk%28x-1%29)
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)
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)
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)
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
4/3
联立y^2=4x y=k(x-1) =>y^2=4(y/k+1) =>ky^2-4y-4k=0
|y1-y2|^2=(y1+y2)^2-4y1y2=(4/k)^2+16=64 =>k=±√3/3
y²=4x => x=y²/4
y=k(x-1) => x=(y+k)/k
∴y²/4=(y+k)/k
ky²-4y²-4k=0
y1+y2=4/k y1*y2=-4
|y1-y2│=8 => (y1-y2)²=(y1+y2)²-4y1y2=64
k²=1/3
k=±√1/3
∵ y²=4x => x=y²/4
y=k(x-1) => x=(y+k)/k
∴y²/4=(y+k)/k
变换得 ky²-4y²-4k=0
∴ y1+y2=4/k y1*y2=-4
又∵│y1-y2│=8 => (y1-y2)²=(y1+y2)²-4y1y2=64
∴k²=1/3
k=±√1/3
y²=4x => x=y²/4
y=k(x-1) => x=(y+k)/k
∴y²/4=(y+k)/k
ky²-4y²-4k=0
y1+y2=4/k y1*y2=-4
|y1-y2│=8 => (y1-y2)²=(y1+y2)²-4y1y2=64
k²=1/3
k=±√1/3