Question

va rog să mă ajutați ​

Answer 1

$a) f(-4)=2*(-4)^{2} -3=32-3=29\\f(\frac{1}{2} )=2\\f(5)=3*5-6=15-6=9\\f(\frac{1}{\sqrt{2}} ) = 2\\f(0) = 2\\f(-\sqrt{3} )=2*(-\sqrt{3})^{2} - 3 = 2*3-3=3\\f(10)=3*10-6=30-6=24$

$f(1)+f(2)+...+f(n)=105\\3*1-6+3*2-6+...+3n-6=105\\3(1+2+...+n)-6n=105\\\frac{3n(n+1)}{2} - 6n =105\\ 3n(n+1)-12n=210\\3n^{2} + 3n -12n - 210 = 0 \\3n^{2} - 9n - 210 = 0\\simplificam prin 3\\n^{2}-3n-70=0\\delta=(-3)^{2} - 4(-70)=9+280=289=17^{2} \\delta > 0, deci x_{1,2}= \frac{3+-\sqrt{17^{2} } }{2} \\dar x este numar natural\\deci x=\frac{3+17}{2}=20:2=10$