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Hey

Id appreciate some help with these questions:

(A) [tex]\alpha,\beta[/tex] are roots of the equation [tex]x^2 - 2lx + m = 0[/tex]. Show that [tex]\alpha^2 + \beta^2 = 2(2l^2 - m)[/tex]. Express [tex]\alpha^4 + \beta^4[/tex]in terms of [tex]l and m[/tex].

Ive shown that [tex]\alpha^2 + \beta^2 = 2(2l^2 - m)[/tex], but im having trouble figuring out what [tex]\alpha^4 + \beta^4[/tex] is - i was thinking [tex](\alpha^2 + \beta^2)^2[/tex], but this didnt seem right. Any ideas?

(B)The vertices of a rectangle lie on a circle of radius = a.

Show that the area of the rectangle is not greater than [tex]2a^2[/tex].

Im lost as to how i should answer this one. Any help is appreciated.

Id appreciate some help with these questions:

(A) [tex]\alpha,\beta[/tex] are roots of the equation [tex]x^2 - 2lx + m = 0[/tex]. Show that [tex]\alpha^2 + \beta^2 = 2(2l^2 - m)[/tex]. Express [tex]\alpha^4 + \beta^4[/tex]in terms of [tex]l and m[/tex].

Ive shown that [tex]\alpha^2 + \beta^2 = 2(2l^2 - m)[/tex], but im having trouble figuring out what [tex]\alpha^4 + \beta^4[/tex] is - i was thinking [tex](\alpha^2 + \beta^2)^2[/tex], but this didnt seem right. Any ideas?

(B)The vertices of a rectangle lie on a circle of radius = a.

Show that the area of the rectangle is not greater than [tex]2a^2[/tex].

Im lost as to how i should answer this one. Any help is appreciated.

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