Question 77271
{{{a/b + (a + 10b)/(b + 10a) = 2}}}
{{{ab/b + (a + 10b)b/(b + 10a) = 2b}}}
{{{a + (a + 10b)b/(b + 10a) = 2b}}}
{{{a(b + 10a) + (a + 10b)b(b + 10a)/(b + 10a) = 2b(b + 10a)}}}
{{{a(b + 10a) + (a + 10b)b = 2b(b + 10a)}}}
{{{ab + 10a^2 + ab + 10b^2 = 2b^2 + 20ab}}}
{{{10a^2 - 18ab + 8b^2 = 0}}}
{{{10a^2 - 10ab - 8ab + 8b^2 = 0}}}
{{{(10a^2 - 10ab) + (-8ab + 8b^2) = 0}}}
{{{10a(a - b) - 8b(a - b) = 0}}}
{{{(10a - 8b)(a - b) = 0}}}
we get: 10a - 8b = 0
10a = 8b
a = .8b and b = 1.25a
a / b or .8b / 1.25a or .8(1.25a) / 1.25a = 0.8
we get: a - b = 0
a = b
a / b = b / b = 1
(d)