Đáp án:
c/ S={0;$\frac{2}{3}$)
d/ S={38;18}
Giải thích các bước giải:
Bài 3:
c/ √1-2x² = x-1
⇔ (√1-2x²)² = (x-1)²
⇔ 1-2x² = x²-2x+1
⇔ -2x²-x²+2x=1-1
⇔ -3x²+2x=0
⇔ -x(3x-2)=0
⇔ \(\left[ \begin{array}{l}-x=0\\3x-2=0\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=0\\3x=2\end{array} \right.\)
⇔ x=0 hoặc x=2/3
Vậy S={0;$\frac{2}{3}$)
d/ √x-1-2√x-2=5
⇔ (√x-1-2√x-2)²=5²
⇔ x-1-2√x-2=25
⇔ x-2√x-2=26
⇔ 2√x-2=26-x
⇔ (2√x-2)²=(26-x)²
⇔ 4(x-2)=(26-x)²
⇔ 4x-8=26²-2.26x+x²
⇔ -x²+4x+2.26x-8-26²=0
⇔ -x²+56x-684=0
⇔ -x²+38x+18x-684=0
⇔ -x(x-38)+18(x-38)=0
⇔ (x-38)(-x+18)=0
⇔ \(\left[ \begin{array}{l}x-38=0\\-x+18=0\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=38\\-x=-18\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=38\\x=18\end{array} \right.\)
Vậy S={38;18}
