Question

Determine os valores das constantes reais a e b que satisfazem:

(ax+5)2+(b-2x)2=13 x2+42x+34

Answer 1

(ax+5)2+(b-2x)2=13 x2+42x+34
 a^2x^2 +10ax +25 +b^2-4bx +4x^2 = 13 x2+42x+34
 a^2x^2 + 4x^2 + 10ax - 4bx +b^2 +25 = 13 x2+42x+34 

a^2 + 4 =  13 ==> a^2 =13 - 4 ==> a^2 = 9 ==> a= +/-V9 ==> a = +/- 3
10a - 4b = 42 ==> 10a = 42 + 4b ==> a = ( 42 + 4b)/10
b^2 + 25 = 34 ==> b^2 = 34-25 ==> b^2 = 9 ==> b = +/-3