Giải thích các bước giải:

Gọi $AB=x, 0<x<9$

$\to BH=9-x$

$\to BC=\sqrt{CH^2+HB^2}=\sqrt{6^2+(9-x)^2} =\sqrt{x^2-18x+117}$

Theo bài ta có:

$50000\cdot \sqrt{x^2-18x+117}+(9-x)\cdot 130000=1170000$

$\to 50000\cdot \sqrt{x^2-18x+117}=1170000-(9-x)\cdot 130000$

$\to 50000\cdot \sqrt{x^2-18x+117}=130000x$

$\to 5\cdot \sqrt{x^2-18x+117}=13x$

$\to 25x^2-450x+2925=169x^2$

$\to -144x^2-450x+2925=0$

$\to x=\dfrac{-25\pm5\sqrt{233}}{16}$

$\to x=\dfrac{5\left(\sqrt{233}-5\right)}{16}$ vì $x>0$

$\to AB=x\approx 3.2$