Question

Calculati:
Radical din 4x^2 -4x+1 -5=0

Va rog mult, macar o idee.
App, -5 nu este sub radical.

Answer 1

$\displaystyle \sqrt{4x^2-4x+1}-5=0 \\ \sqrt{4x^2-4x+1} =0+5 \\ \sqrt{4x^2-4x+1} =5 \\ \left( \sqrt{4x^2-4x+1} \right)^2=5^2 \\ 4x^2-4x+1=25 \\ 4x^2-4x+1-25=0 \\ 4x^2-4x-24=0|:4 \\ x^2-x-6=0 \\ a=1,~b=-1,~c=-6 \\ \Delta=b^2-4ac=(-1)^2-4 \cdot 1 \cdot (-6)=1+24=25\ \textgreater \ 0 \\ x_1= \frac{1+ \sqrt{25} }{2 \cdot 1} = \frac{1+5}{2} = \frac{6}{2} =3 \\ x_2= \frac{1- \sqrt{25} }{2 \cdot 1} = \frac{1-5}{2} = \frac{-4}{2} =-2$