GPT : $\sqrt{x-1}+2\sqrt{x^2-9}=10$

$\textit{Đáp án + Giải thích các bước giải:}$

`\sqrt{x-1}+2\sqrt{x^2-9}=10` `(x \ge 3)`

`<=>(\sqrt{x-1}-2)+(2\sqrt{x^2-9}-8)=0`

`<=>((\sqrt{x-1})^2-2^2)/(\sqrt{x-1}+2)+(2((\sqrt{x^2-9})^2-4^2))/(2(\sqrt{x^2-9}+8))=0`

`<=>(x-5)/(\sqrt{x-1}+2)+(2(x^2-9-16))/(2\sqrt{x^2-9}+8)=0`

`<=>(x-5)/(\sqrt{x-1}+2)+(2(x-5)(x+5))/(2\sqrt{x^2-9}+8)=0`

`<=>(x-5)(1/(\sqrt{x-1}+2)+(2(x+5))/(2\sqrt{x-9}+8))=0`

Vì `1/(\sqrt{x-1}+2)+(2(x+5))/(2\sqrt{x-9}+8)>0 \forall x` tmđk `<=>x-5=0<=>x=5` $(tm)$

Vậy `x=5`