[tex3]
P(x)\!=x^4\!\!+\!ax^3\!\!+\!bx^2\!\!+\!cx\!+\!d=(x\!-\!r_1)(x\!-\!r_2)(x\!-\!r_3)(x\!-\!r_4)\quad\text{com }r_1,r_2,r_3,r_4\text{ raízes de }P(x)\!=\!0\text{ e }r_1r_2\!=\!r_3r_4\!=\!r\\
\text{Temos:}\\
a=-(r_1+r_2+r_3+r_4)\\
c=-(r_1r_2r_3+r_1r_2r_4+r_1r_3r_4+r_2r_3r_4)=-(rr_3+rr_4+rr_1+rr_2)=-r(r_1+r_2+r_3+r_4)=ra\\
\text{e então }c^2=r^2a^2=da^2\quad\text{já que }d=r_1r_2\cdot r_3r_4=r^2\\[12pt]
\boxed{\ \\[3pt]\hspace{1cm}c^2=da^2\hspace{1cm}\\}
[/tex3]
[tex3]
P(x)\!=x^4\!\!+\!ax^3\!\!+\!bx^2\!\!+\!cx\!+\!d=(x\!-\!r_1)(x\!-\!r_2)(x\!-\!r_3)(x\!-\!r_4)\quad\text{com }r_1,r_2,r_3,r_4\text{ raízes de }P(x)\!=\!0\text{ e }r_1r_2\!=\!r_3r_4\!=\!r\\
\text{Temos:}\\
a=-(r_1+r_2+r_3+r_4)\\
c=-(r_1r_2r_3+r_1r_2r_4+r_1r_3r_4+r_2r_3r_4)=-(rr_3+rr_4+rr_1+rr_2)=-r(r_1+r_2+r_3+r_4)=ra\\
\text{e então }c^2=r^2a^2=da^2\quad\text{já que }d=r_1r_2\cdot r_3r_4=r^2\\[12pt]
\boxed{\ \\[3pt]\hspace{1cm}c^2=da^2\hspace{1cm}\\}
[/tex3]
Se \alpha \in ]\frac{\pi }{2},\pi [ tal que 5(sen^2\alpha +cos^2\theta )+6cos\theta =2(sen\alpha -1) . Então, o valor de M, tal que M=2\sqrt{6}tg\alpha +cos\theta vale
a) -8/5
b) -7/5
c) -6/5
d)...
O valor da expressão
M=\left(tg\left(\frac{2\pi }{9}\right)+2tg\left(\frac{\pi }{18}\right)\right)tg\left(\frac{7\pi }{9}\right)
é igual a:
a) -1
b) 2
c) raiz quadrada de 7
d) (raiz quadrada de 7)...