1. a·b = 375
(a+5)(b-5) = 400 ab +5(a-b) -25 = 400 375 +5(a-b) = 425 ⇒ a - b = 10
b = a - 10 a(a-10) = 375 a² -10a - 375 = 0 a² -25a + 15a - 375 = 0
a(a-25) + 15(a - 25) = 0 (a-25)(a+15) = 0
a-25 = 0 a = 25 b = 15
a+15 = 0 a = -15 b = -25
2. x+y = 23 3x + 3y = 69
3x + 7y = 113 4y = 44 y = 11 x = 12
3. 3²ˣ + 2ₓ3ˣ = 99
daca 3ˣ = y y² +2y - 99 = 0 y - 9y + 11y - 99 = 0 y(y-9) + 11(y-9) = 0
(y-9)(y +11) = 0 y-9 = 0 y = 9 3ˣ = 3² x = 2
y +11 = 0 y = -11 3ˣ = -11 xlg3 = lg(-11) ∉ R
4. 2(10a +b) + 2(10b + a) = 22a + 22b = ????