If `a,b in I` and satisfy the equation `a(b-1)=3+b-b^(2),` then find the greatest value of `|a+b|`

If a, b in R satisfy the equation a^(2)+4b^(2)-4=0 , then the minimum value of (2a+3b) will be

If a/b=2/3 then find the values of b/a

If a, b and c satisfy the equation x^(3)-3x^(2) + 2x+1 =0 then what is the value of (1)/(a)+(1)/(b)+(1)/(c ) ?

3.If a+b=6 then find the value of 1/2a+1/2b

If (2a+b)/(a +4b)=3 , then find the value of (a+b)/(a+2b)

If a/b=2/3 then find the values of (4a+3b)/(3b)

If (2a+b)/(a+4b)=3, then find the value of (a+b)/(a+2b)

(2) If a=-2 , b=-3 , then find the value of (b/a-a/b)^a

If (2a+ b)/(a+4b) = 3 , then find the value of (a+b)/(a+2b)

(i) If a + b + c = 5 , (a, b, c gt 0) , find the greatest value of a^(3) b^(2) c^(4) . (ii) Find the greatest value of (5 - x)^(2) (x -2)^(2) , given 2 lt x lt 5 .