Đáp án:
Giải thích các bước giải:
Đk x≥3
$\sqrt[]{x(x-1)}$ +$\sqrt[]{x(x-2)}$ =2$\sqrt[]{x(x-3)}$
⇔x(x-1)+x(x-2)+2$\sqrt[]{x^2(x-1)(x-2)}$ =4x(x-3)
⇔x²-x+x²-2x+2$\sqrt[]{x^2(x-1)(x-2)}$=4x²-12x
⇔2x²-3x+2$\sqrt[]{x^2(x-1)(x-2)}$=4x²-12x
⇔2$\sqrt[]{x^2(x-1)(x-2)}$=2x²-9x
⇔4x²(x-1)(x-2)=(2x²-9x)² (đk x²(x-1)(x-2)≥0)
⇔(4x³-4x²)(x-2)=4x^4-36x³+81x²
⇔4x^4-8x³-4x³+8x²=4x^4-36x³+81x²
⇔24x³-73x²=0
⇔\(\left[ \begin{array}{l}x=73/24\\x=0\end{array} \right.\)
