Question

cho a,b khác 0, a²-2ab-3b²=0. tính A=(7a+2b)/(2a+b)+(9a-5b)/(2a-b)

Answer 1

a^2 - 2ab - 3b^2 = 0

<=> a^2 - 3ab + ab - 3b^2 = 0

<=> a(a - 3b) + b(a - 3b) = 0

<=> (a - 3b)(a + b) = 0

=> a - 3b = 0 hoặc a + b = 0

=> a = 3b hoặc a = -b

+ Nếu a = 3b

A = (7a+2b)/(2a+b) + (9a-5b)/(2a-b)

A = (7.3b+2b)/(2.3b+b) + (9.3b-5b)/(2.3b-b)

A = 23b/7b + 22b/5b

A = 23/7 + 22/5 = 269/35

+ Nếu a = -b

A = (7a+2b)/(2a+b) + (9a-5b)/(2a-b)

A = (-7b+2b)/(-2b+b) + (-9b-5b)/(-2b-b)

A = -5b/-b + (-14b/-3b)

A = 5 + 14/3 = 29/3