Question

hãy giải phương trình

(x+9)(x+10)(x+11)(x+12)=170

Answer 1

Ta có : \(\left(x+9\right)\left(x+10\right)\left(x+11\right)\left(x+12\right)=170\)

\(\Leftrightarrow\left[\left(x+9\right)\left(x+12\right)\right]\left[\left(x+10\right)\left(x+11\right)\right]=170\)

\(\Leftrightarrow\left(x^2+21x+108\right)\left(x^2+21x+110\right)=170\)

Đặt \(x^2+21x+109=a\).Khi đó , PT tương đương với :

\(\left(a-1\right)\left(a+1\right)=170\)

\(\Leftrightarrow a^2-1=170\)

\(\Leftrightarrow a^2=171\)

Chỗ này thì tớ nghĩ đề sai , 170 phải là 168

Answer 2

\(\left(x+9\right)\left(x+10\right)\left(x+11\right)\left(x+12\right)=170\)

\(\Leftrightarrow\left(x+9\right)\left(x+12\right)\left(x+10\right)\left(x+11\right)=170\)

\(\Leftrightarrow\left(x^2+21x+108\right)\left(x^2+21x+110\right)=170\)

Đặt \(x^2+21x+108=t\)

\(\Leftrightarrow t\left(t+2\right)=170\Leftrightarrow t^2+2t-170=0\)

\(\Leftrightarrow t=1\pm3\sqrt{19}\)đề sai ?