Question

1.Solutia ecuatiei (x-5)(x+5)-(x-3)=x-9

Answer 1

$\displaystyle (x-5)(x+5)-(x-3)=x-9 \\ x^2-25-x+3=x-9 \\ x^2-x-x=-9+25-3 \\ x^2-2x=13 \\ x^2-2x-13=0 \\ a=1,b=-2,c=-13 \\ \Delta=b^2-4ac=2^2-4 \cdot 1 \cdot (-13)=4+52=56\ \textgreater \ 0 \\ x_1= \frac{2+2 \sqrt{14} }{2 \cdot 1} = \frac{2+2 \sqrt{14} }{2} = \frac{\not2(1+ \sqrt{14} )}{\not2} =1+ \sqrt{14} \\ \\ x_2= \frac{2-2 \sqrt{14} }{2 \cdot 1} = \frac{2-2 \sqrt{14} }{2} = \frac{\not2(1- \sqrt{14} )}{\not2} =1- \sqrt{14}$