Đáp án:
Giải thích các bước
x2−xx2−x+1−x2−x+2x2−x−2=1x2−xx2−x+1−x2−x+2x2−x−2=1
→x2−xx2−x+1−1=x2−x+2x2−x−2→x2−xx2−x+1−1=x2−x+2x2−x−2
→x2−x−(x2−x+1)x2−x+1=x2−x+2x2−x−2→x2−x−(x2−x+1)x2−x+1=x2−x+2x2−x−2
→−1x2−x+1=x2−x+2x2−x−2→−1x2−x+1=x2−x+2x2−x−2
Đặt x2−x=ax2−x=a
→−1a+1=a+2a−2→−1a+1=a+2a−2
→−1⋅(a−2)=(a+1)(a+2)→−1⋅(a−2)=(a+1)(a+2)
→a2+4a=0→a2+4a=0
→a∈{0,−4}→a∈{0,−4}
+)a=0→x2−x=0→x∈{1,0}+)a=0→x2−x=0→x∈{1,0}
+)a=−4→x2−x=−4→x2−x+4=0→(x−12)2+4−14=0→
x2−xx2−x+1−x2−x+2x2−x−2=1x2−xx2−x+1−x2−x+2x2−x−2=1
→x2−xx2−x+1−1=x2−x+2x2−x−2→x2−xx2−x+1−1=x2−x+2x2−x−2
→x2−x−(x2−x+1)x2−x+1=x2−x+2x2−x−2→x2−x−(x2−x+1)x2−x+1=x2−x+2x2−x−2
→−1x2−x+1=x2−x+2x2−x−2→−1x2−x+1=x2−x+2x2−x−2
Đặt x2−x=ax2−x=a
→−1a+1=a+2a−2→−1a+1=a+2a−2
→−1⋅(a−2)=(a+1)(a+2)→−1⋅(a−2)=(a+1)(a+2)
→a2+4a=0→a2+4a=0
→a∈{0,−4}→a∈{0,−4}
+)a=0→x2−x=0→x∈{1,0}+)a=0→x2−x=0→x∈{1,0}
+)a=−4→x2−x=−4→x2−x+4=0→(x−12)2+4−14=0→
