Distance problem 2

A=(x,2x)
B=(2x,1)
Distance AB=√2, find value of x

Correct result:

x₁ =  1
x₂ =  -0.2

Solution:

$$\begin{gathered} (x-2x{)}^2+(2x-1{)}^2=2 \\ (x-2x{)}^2+(2x-1{)}^2=2 \\ 5x^2-4x-1=0 \\ a=5;b=-4;c=-1 \\ D=b^2-4ac=4^2-4\cdot 5\cdot (-1)=36 \\ D>0 \\ {x}_{1,2}={\displaystyle \frac{-b\pm \sqrt{D}}{2a}}={\displaystyle \frac{4\pm \sqrt{36}}{10}} \\ {x}_{1,2}={\displaystyle \frac{4\pm 6}{10}} \\ {x}_{1,2}=0.4\pm 0.6 \\ {x}_1=1 \\ {x}_2=-0.2 \\ \text{ Factored form of the equation: } \\ 5(x-1)(x+0.2)=0 \\ {x}_1=1 \end{gathered}$$

Our quadratic equation calculator calculates it.

$x_2=(-0.2)=-{\displaystyle \frac{1}{5}}=-0.2$

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