Đáp án:
x2+2x+1x2+2x+2+x2+2x+2x2+2x=76x2+2x+1x2+2x+2+x2+2x+2x2+2x=76
Đặt x2+2x+1=t→t=(x+1)2≥0x2+2x+1=t→t=(x+1)2≥0
→tt+1+t+1t−1=76→tt+1+t+1t-1=76
→tt+1⋅6(t+1)(t−1)+t+1t−1⋅6(t+1)(t−1)=76⋅6(t+1)(t−1)→tt+1⋅6(t+1)(t−1)+t+1t−1⋅6(t+1)(t−1)=76⋅6(t+1)(t−1)
→6t(t−1)+6(t+1)2=7(t+1)(t−1)→6t(t−1)+6(t+1)2=7(t+1)(t−1)
→12t2+6t+6=7t2−7→12t2+6t+6=7t2−7
→5t2+6t+13=0→5t2+6t+13=0
→4t2+(t+3)2+4=0→4t2+(t+3)2+4=0
→→ Phương trình vô nghiệm