Question

find the positive value of a and b ,when (a+b)/a = b, where a not equal to b .​

Answer 1

Step-by-step explanation:

math]a+b = a/b + b/a[/math]

-> Now take L.C.M

[math]a+b = (a^2 + b^2)/ab[/math]

-> Cross multiplying

[math](a+b)ab = a^2 + b^2[/math]

[math]a^2.b + b^2.a = a^2 + b^2[/math]

Take [math]a^2[/math] and [math]b^2[/math] common

[math]a^2(b-1) + b^2(a-1) = 0 [/math] --(1)

Now since [math]a [/math] and [math]b [/math] are positive integers - their square can’t be zero.

So in order to make the equation 1 equal to zero:

[math](b-1)[/math] and [math](a-1) [/math]both has to be [math]0[/math].

Therefore,

[math]b-1 = 0[/math] =>[math]b=1[/math]

and,

[math]a-1 = 0[/math] =>[math]a=1[/math]

Hence [math]a = b = 1[/math]