If `a , b` are two real numbers with a`<`b then a real number `c` can be found between `a and b` such that the value of `(a^2+a b+b^2)/(c^2)i s_____`

Answer

4

Explanation

Let `f(x)=x^(4),xepsilon[a,b]`
`f(x)` satisfies coditions of `LMVT` [as `f(x)` is continuous and differentiable] therefore.
`(f(b)-f(a))/(b-a)=f^(')(c),agtcgtb`
or `(b^(4)-a^(4))/(b-a)=4c^(3)implies((b^(2)+a^(2))(b+a)(b-a))/((b-a)^(c^(3)))=4`
`(b^(3)+a^(3)+ab^(2)+a^(2)b)/(c^(3))=4`