Question

cho phuong trinh \(x^2-4x+m+1=0\)

a) tim m de phuong trinh co ngiem.

b) tim m de phuong trinh co ngiem \(x_1,x_2\) thoa man:\(x_1^2+x^2_2=10\).

c) tim m de phuong trinh co hai ngiem \(x^2_1,x^2_2\) thoa man:\(x_1^3+x_2^3=34\).

Answer 1

a) có nghiệm => \(\Delta=16-4\left(m+1\right)=12-4m\ge0\Leftrightarrow m\le3\)

áp dụng hệ thức vi ét ta có: x1+x2=4;   x1.x2=m+1

b) \(x1^2+x2^2=10\Leftrightarrow\left(x1+x2\right)^2-2x1x2=10\Leftrightarrow16-2\left(m+1\right)=10\Leftrightarrow m=2\)(t/m đk)

c) \(x1^3+x2^3=34\Leftrightarrow\left(x1+x2\right)^3-3x1.x2\left(x1+x2\right)=34\Leftrightarrow64-12\left(m+1\right)=34\Leftrightarrow m=\frac{3}{2}\)(t/m đk)