1. den ta =1-4m+8=0
giải ra
2. áp dụng viet
x1+x2=2-m
x1*x2=-8
ta có x1^2+x2^2=(x1+x2)^2-2x1x2=25
thay vô giải pt ra
denta : 12 - 4.(m-2)= 1-4m+8=9-4m
de pt co nghiem kep thi : den ta = 0 <=> 9-4m = 0 <=> 4m = 9 <=> m = 9/4
thay m=9/4 vao (1) co:
x2 + x + 9/4 - 2 =0 <=> x2 + x + 1/4 = 0
den ta= 12 - 4.1/4 <=> denta= 1-1 <=> denta = 0
=> pt co nghiem kep x1 = x2 = -1/2
vay.....
2. x2 + (m-2)x - 8 = 0
denta = (m-2)2- 4(-8)<=> denta = (m-2)2+32
vi (m-2)2 >= 0 V m => (m-2)2 +32 >/ 32 Vm => denta > 0 V m => pt luon co 2 nghiem pb
V m pt luon co 2 nghiem pb
theo ht viet ta co
x1 + x2 = -m+2
x1.x2 = -8
theo de bai ra ta co :
x12 + x22 = 25 <=> (x1+x2)2 - 2x1x2 = 25 <=> (-m+2)2 - 2 (-8) = 25 <=> m2+4m+4+16-25=0<=> m2+4m-5=0
ta co: a+b+c=1+4+(-5)=1+4-5=0
=. pt co 2 ngiem pb
m1 = 1
m2 = -5
vay m = 1& m=-5 thi pt co 2 nghiem t/m : x12 + x22 = 25