Question

giải cac phương trình:

a) \(x+\sqrt{x-15}=17\)

b) \(\left(x-1\right)\left(x-2\right)\left(x-3\right)\left(x-4\right)=0\)

c)\(\left(x^2+x+1\right)\left(x^2+x+12\right)=12\)

d) \(\frac{24}{x^2+2x-8}-\frac{15}{x^2+2x-3}=2\)

Answer 1

\(\Leftrightarrow x-16+\sqrt{x-15}-1=0\)0

\(\Leftrightarrow x-16+\frac{x-16}{\sqrt{x-15}+1}\)= 0

\(\Leftrightarrow\left(x-16\right)\cdot\left(1+\frac{1}{\sqrt{x-15}+1}\right)\)=0

Answer 2

b)\(\Leftrightarrow\left(x^2-5\cdot x+4\right)\cdot\left(x^2-5\cdot x+6_{ }\right)=0\)

Đật T=\(x^2-5\cdot x+4\)

C) dat T= \(x^2+x+1\)

Answer 3

d) dat t=\(x^2+2\cdot x-3\)

Answer 4

a)Cách 2: (có lẽ không cần dùng liên hợp)

Đặt \(\sqrt{x-15}=t\ge0\).Ta có:

\(PT\Leftrightarrow\left(x-15\right)+\sqrt{x-15}-2=0\)

\(\Leftrightarrow t^2+t-2=0\Leftrightarrow\orbr{\begin{cases}t=1\\t=-2\left(L\right)\end{cases}}\)

\(t=1\Rightarrow\sqrt{x-15}=1\Rightarrow x=16\)