Răspuns:
Mg(a,b) = rad(a*b)
a) x = (rad(2)-1)(3+rad(5))(rad(7)-rad(6))(4 + rad(7))
y = (rad(2)+1)(3-rad(5))(rad(7)+rad(6))(4-rad(7))
Mg(x, y) =
= rad(xy)
Reordonam factorii in mod convenabil. Ne folosim de formula (a+b)(a-b) = a^2-b^2
(rad(2)-1)(rad(2)+1) = 2-1 = 1
(3+rad(5))(3-rad(5)) = 9-5 = 4
(rad(7)-rad(6))(rad(7)+rad(6)) = 7-6 = 1
(4+rad(7))(4-rad(7)) = 16-7 = 9
Mg(x, y) = rad(9*4) = 3*2 = 6
De acum scriu r() in loc de rad().
b) x = r(7-4r(3))
Inauntrul radicalului se observa un binom, in care nr vor fi a si b.
a^2 + b^2 = 7
2ab = 4r(3)
ab = 2r(3)
Prin incercari se afla a=2, b=r(3)
x = r((2-r(3))^2)
x = |2 - r(3)|
2 > r(3) =>
x = 2 - r(3)
Analog pt y, a.î. avem y = 2 + r(3)
Mg(x, y) =
= r(xy) =
= r((2-r(3))(2+r(3))) =
= r(4 - 3) =
= r(1) =
= 1
c) x = r((3+2r(3))^2)
x = |3 + 2r(3)|
x = 3 + 2r(3)
y se bazeaza pe aceeasi teorie ca la punctul b.
a^2 + b^2 = 21
2ab = 12r(3)
ab = 6r(3)
a = 3, b = 2r(3)
y = r((2r(3)-3)^2)
y = |2r(3) - 3|
2r(3) > 3
y = 2r(3) - 3
x = 2r(3)+3
xy = 12 - 9 = 3
Mg(x,y) = rad(xy) = rad(3)
