Question

a•b=375 si (a+5)•(b-5)=400 cat e a cat e b

Answer 1

(a+5) × (b-5) = 400
a × b + 5b - 5a - 25 = 400
375 + 5×(b - a - 5) = 400
5×(b-a-5) = 400 - 375 = 25
b - a - 5 = 25 : 5 = 5
b - a = 5 + 5
b - a = 10 (1)
a × b = 375
a = 375 : b
inlocuim pe a in relatia (1)
b - 375 : b = 10 |×b
b^2 - 375 = 10b
b^2 - 10b - 375 = 0
delta = 100+4×375 =
= 100+1500 =
= 1600
b1,2 = (10+-40)/2 = 5+-20

b1 = 25
b2 = -15

a1 = 375 : 25 = 15
a2 = 375 : (-15) = -25