Question

Determine os valores das constantes reais a e b que satisfazem (ax+5)^2 + (b-2x)^2 = 13x^2 + 42x + 34 

 

Answer 1

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

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

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

a^2 + 4 = 13 ==> a^2 = 9 ==> a= +/- 3

10a - 4b = 42

a1=3 ==> 10.3 - 4b1 =42 ==> 4b1 = - 42 + 30==> 4b1 = - 12  ==> b1 = - 3

a2= - 3 ==> 10.(-3) - 4b2 =42 ==> 4b2 = - 42 - 30==> 4b2 = - 72  ==> b2 = - 18