Find the maximum value of the expression `(a^2+b^2)/(a^2+3ab+5b^2)`

Let alpha,beta,gamma be distinc real numbrs such that a alpha^(2)+b alpha+c=(sin theta)alpha^(2)+(cos theta)alphaa beta^(2)+boldsymbol eta+c=(sin theta)beta^(2)+(cos theta)gammaa gamma^(2)+b gamma+c=(sin theta)gamma^(2)+(cos theta)gamma Find the maximum value of he expression (a^(2)+b^(2))/(a^(2)+3ab+5b^(2))

If a/b=2/3 then find the values of expressions: (5a^2+2b^2)/(5a^2-2b^2)

Find the value of the expression: a^2-ab-2a+5b when a=2 and b=-3

When a = 0, b = – 1, find the value of the given expressions 2a^2b + 2ab^2 + ab

When a=0, b=-1, find the value of the given expressions: 2a^2b+2ab^2+ab

Find the sum of the expressions - 3a ^(2) + 2 ab - 4b^(2) and - 6a ^(2) + 4b.