Question

sa se det m apartine R stiind ca inec 4x²-2(m+1)x+m≥0 e verificata pentru orice x apartine R

Answer 1

4x²-2(m+1)x+m≥0
a=4
b=2(m+1)
c=m
Δ=b²-4ac⇒[2(m+1)]²-4×4×m⇒Δ=(2m+2)²-16m⇒Δ=(4m²+8m+4)-16m⇒Δ=
4m²+8m+4-16m=0⇒4m²-8m+4=0
a=4
b=-8
c=4
Δ=b²-4ac⇒Δ=(-8)²-4×4×4⇒64-64⇒0
x1x2=-b+-√Δ/2a⇒
m1=8+0/8⇒8/8⇒m1=1
m2=8-0/8⇒8/8⇒m2=1

sucees