Question

giai pt

 

\(\sqrt{x+1}+\sqrt{x+16}=\sqrt{x+4}+\sqrt{x+9}\)

Answer 1

Điều kiện xác định tự làm nha:

\(\sqrt{x+1}+\sqrt{x+16}=\sqrt{x+4}+\sqrt{x+9}\)

\(\Leftrightarrow2x+17+2\sqrt{\left(x+1\right)\left(x+16\right)}=2x+13+2\sqrt{\left(x+4\right)\left(x+9\right)}\)

\(\Leftrightarrow2+\sqrt{\left(x+1\right)\left(x+16\right)}=\sqrt{\left(x+4\right)\left(x+9\right)}\)

\(\Leftrightarrow4+x^2+17x+16+4\sqrt{\left(x+1\right)\left(x+16\right)}=x^2+13x+36\)

\(\Leftrightarrow\sqrt{\left(x+1\right)\left(x+16\right)}=-x+4\)

Điều kiện: \(x\le4\)

\(\Leftrightarrow x^2+17x+16=x^2-8x+16\)

\(\Leftrightarrow25x=0\)

\(\Leftrightarrow x=0\)