Explicație pas cu pas:
[tex]f(x) = x - 3[/tex]
a) observăm că:
[tex]f( \sqrt{9} ) = f(3) = 3 - 3 = 0[/tex]
=>
[tex]f( \sqrt{7} ) \times f( \sqrt{8} ) \times f( \sqrt{9} ) \times f( \sqrt{10} ) \times f( \sqrt{11} ) = 0[/tex]
b) P(-2, 0)
[tex]y = x - 3 => x - y - 3 = 0[/tex]
[tex]d = \frac{ |ax_{P} + by_{P} + c| }{ \sqrt{{a}^{2} + {b}^{2}}} \\ = \frac{ |1 \times ( - 2) + ( - 1) \times 0 + ( - 3)| }{ \sqrt{ {1}^{2} + {( - 1)}^{2} } } \\ = \frac{ | - 2 - 3| }{ \sqrt{2} } = \frac{ | - 5| }{ \sqrt{2} } = \frac{5}{ \sqrt{2} } = \frac{5 \sqrt{2} }{2} [/tex]
