Question

Giải pt bậc 2 một ẩn : ( 1 + sqrt(2) ) x mũ 2 - x - sqrt(2) =0

Answer 1

\(\left(1+\sqrt{2}\right)x^2-x-\sqrt{2}=0\)

\(\Leftrightarrow\left(1+\sqrt{2}\right)x^2-x-\sqrt{2}x-\sqrt{2}=0\)

\(\Leftrightarrow\left(1+\sqrt{2}\right)x^2-x\left(1+\sqrt{2}\right)+\sqrt{2}\left(x-1\right)=0\)

\(\Leftrightarrow\left(1+\sqrt{2}\right)x\left(x-1\right)+\sqrt{2}\left(x-1\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x+\sqrt{2}x+\sqrt{2}\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=1\\x=-2+\sqrt{2}\end{cases}}\)

Chúc bạn học tốt !!!