a)PT có nghiệm
`<=>Delta'>=0`
`<=>1-(m-1)>=0`
`<=>m-1<=1`
`<=>m<=2`
b)Áp dụng vi-ét ta có:
`x_1+x_2=2,x_1.x_2=m-1`
`A=(x_1+x_2)(x_1^2-x_1.x_2+x_2^2)`
`=2[(x_1+x_2)^2-3x_1.x_2]`
`=2[4-3(m-1)]`
`m<=2=>m-1<=1`
`=>3(m-1)<=3`
`=>4-3(m-1)>=1`
`=>A>=2.1=2`
Dấu "=" `<=>m=2`
a,
PT có nghiệm
⇔Δ'≥0⇔Δ′≥0
⇔1−(m−1)≥0⇔1-(m-1)≥0
⇔m−1≤1⇔m-1≤1
⇔m≤2
b,
Áp dụng vi-ét ta có:
x1+x2=2,x1.x2=m−1x1+x2=2,x1.x2=m-1
A=(x1+x2)(x21−x1.x2+x22)A=(x1+x2)(x12-x1.x2+x22)
=2[(x1+x2)2−3x1.x2]=2[(x1+x2)2-3x1.x2]
=2[4−3(m−1)]=2[4-3(m-1)]
m≤2⇒m−1≤1m≤2⇒m-1≤1
⇒3(m−1)≤3⇒3(m-1)≤3
⇒4−3(m−1)≥1⇒4-3(m-1)≥1
⇒A≥2.1=2⇒A≥2.1=2
Dấu "=" ⇔m=2
