1, Ta có: \(\Delta=\left(-7\right)^2-4.1.m=49-4m\)
Để pt có nghiệm thì \(\Delta\ge0\)
\(\Leftrightarrow49-4m\ge0\\ \Leftrightarrow4m\le49\\ \Leftrightarrow m\le\dfrac{49}{4}\)
2, Theo Vi-ét ta có:\(\left\{{}\begin{matrix}x_1+x_2=7\\x_1x_2=m\end{matrix}\right.\)
\(x_1^3+x_2^3=91\)
\(\Leftrightarrow\left(x_1+x_2\right)\left(x^2_1-x\text{}_1x_2+x_2^2\right)=91\)
\(\Leftrightarrow\left(x_1+x_2\right)\left[\left(x_1+x_2\right)^2-3x\text{}_1x_2\right]=91\)
\(\Leftrightarrow7\left(7^2-3m\right)=91\)
\(\Leftrightarrow49-3m=13\)
\(\Leftrightarrow3m=36\)
\(\Leftrightarrow m=12\left(tm\right)\)
a, Để pt có 2 nghiệm khi
\(\Delta=49-m\ge0\Leftrightarrow m\le49\)
b, Theo Viet : \(\left\{{}\begin{matrix}x_1+x_2=7\\x_1x_2=m\end{matrix}\right.\)
Ta có : \(x_1^3+x_2^3=\left(x_1+x_2\right)^3-3x_1x_2\left(x_1+x_2\right)\)
\(343-21m=91\Leftrightarrow21m=252\Leftrightarrow m=12\)(tmđk)
a.
\(\Delta=49-4m\ge0\Rightarrow m\le\dfrac{49}{4}\)
b. Theo hệ thức Viet: \(\left\{{}\begin{matrix}x_1+x_2=7\\x_1x_2=m\end{matrix}\right.\)
\(x_1^3+x_2^3=91\)
\(\Leftrightarrow\left(x_1+x_2\right)^3-3x_1x_2\left(x_1+x_2\right)=91\)
\(\Leftrightarrow7^3-21m=91\)
\(\Leftrightarrow m=12\) (t/m)
