Question

-x la a 2+8x-16=0 -x la a 2 -7x+8 =0 3x-7 pe x+5 = x-3 pe x+2 rezolvare completa rapid va rog pls!

Answer 1

$\displaystyle a).-x^2+8x-16=0 \\ x^2-8x+16=0 \\ a=1,b=-8,c=16 \\ \Delta=b^2-4ac=8^2-4 \cdot 1 \cdot 16=64-64=0 \\ x_1=x_2=- \frac{b}{2a} =- \frac{-8}{2 \cdot 1} =- \frac{-8}{2} =-(-4)=4$

$\displaystyle b).-x^2-7x+8=0 \\ x^2+7x-8=0 \\ a=1,b=7,c=-8 \\ \Delta=b^2-4ac=7^2-4 \cdot 1 \cdot (-8)=49+32=81\ \textgreater \ 0 \\ x_1= \frac{-7+ \sqrt{81} }{2 \cdot 1} = \frac{-7+9}{2} = \frac{2}{2} =1 \\ \\ x_2= \frac{-7- \sqrt{81} }{2 \cdot 1} = \frac{-7-9}{2}= \frac{-16}{2} =-8$

$\displaystyle c). \frac{3x-7}{x+5} = \frac{x-3}{x+2} \\ (3x-7)(x+2)=(x+5)(x-3) \\ 3x^2+6x-7x-14=x^2-3x+5x-15 \\ 3x^2+6x-7x-x^2+3x-5x=-15+14 \\ 2x^2-3x=-1 \\ 2x^2-3x+1=0 \\ a=2,b=-3,c=1 \\ \Delta=b^2-4ac=3^2-4 \cdot 2 \cdot 1=9-8=1\ \textgreater \ 0 \\ x_1= \frac{3+ \sqrt{1} }{2 \cdot 2} = \frac{3+1}{4} = \frac{4}{4} =1 \\ \\ x_2= \frac{3- \sqrt{1} }{2 \cdot 2} = \frac{3-1}{4} = \frac{2}{4} ^{(2} = \frac{1}{2}$