Question

tìm x biết :

25(x+1)^4-26(x+1)^2+1=0

x^2+(x-1)=0

\(\dfrac{x+1}{100}\) +\(\dfrac{x+2}{999}+.....+\dfrac{x+6}{995}+5=0\)

4x^2-4x-5(2x-1)-5=0

Answer 1

a: \(\Leftrightarrow25\left(x+1\right)^4-25\left(x+1\right)^2-\left(x+1\right)^2+1=0\)

\(\Leftrightarrow\left[\left(x+1\right)^2-1\right]\left[25\left(x+1\right)^2-1\right]=0\)

\(\Leftrightarrow\left(x+2\right)\cdot x\cdot\left(5x+4\right)\left(5x+6\right)=0\)

hay \(x\in\left\{0;-2;-\dfrac{4}{5};-\dfrac{6}{5}\right\}\)

b: \(x^2+x-1=0\)

\(\text{Δ}=1^2-4\cdot1\cdot\left(-1\right)=5\)

Do đó: PT có 2 nghiệm phân biệt là:

\(\left\{{}\begin{matrix}x_1=\dfrac{-1-\sqrt{5}}{2}\\x_2=\dfrac{-1+\sqrt{5}}{2}\end{matrix}\right.\)

d: \(\Leftrightarrow4x^2-4x+1-5\left(2x-1\right)-6=0\)

\(\Leftrightarrow\left(2x-1\right)^2-5\left(2x-1\right)-6=0\)

=>(2x-1-6)(2x-1+1)=0

=>(2x-7)2x=0

=>x=0 hoặc x=7/2