Question

Rezolvati in R ecuatia:
3√2 x+7=0
16x-3(x+1)=5x
2,5(x-4)-6x=3-x
x²-3x-10=0

Answer 1

$a).\displaystyle 3 \sqrt{2} x+7=0 \\ 3 \sqrt{2} x=0-7 \\ 3 \sqrt{2} x=-7 \\ x=- \frac{7}{3 \sqrt{2} } \\ b).16x-3(x+1)=5x \\ 16x-3x-3=5x \\ 16x-3x-5x=3 \\ 8x=3 \\ x= \frac{3}{8}$
$\displaystyle c).2,5(x-4)-6x=3-x \\ 2,5x-10-6x=3-x \\ 2,5x-6x+x=3+10 \\ -2,5x=13 \\ x=- \frac{13}{2,5} \\ x=-5,2$
$\displaystyle d).x^2-3x-10=0 \\ a=1,b=-3,c=-10 \\ \Delta=b^2-4ac=3^2-4 \cdot 1 \cdot (-10)=9+40=49\ \textgreater \ 0 \\ x_1= \frac{3+ \sqrt{49} }{2 \cdot 1} = \frac{3+7}{2} = \frac{10}{2} =5 \\ \\ x_2= \frac{3- \sqrt{49} }{2 \cdot 1} = \frac{3-7}{2} = \frac{-4}{2} =-2$