A Nice Algebra Question | Math Problem solving | Mathematics | AM-GM Inequality

A Nice Algebra Question | Math Problem solving | Mathematics | AM-GM Inequality

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[mrityunjaykumar]

we can take a+b=x and c+d=4-x, and since a, b, c, d =+ve real nos hence x>=0 and 4-x>=0 => x belongs to (0, 4)
and (a+b)(c+d)=x(4-x)=4x-x^2 which has roots 0, 4 is inverted parabola..hence find max value between roots with Ymax=-D/4a

[jarikosonen]

Also solved with s=a+b, t=c+d, s+t=4,
s*t=s*(4-s), then checked max(4s-s^2)=4 at s=2 (&t=2).

[OlgaPlaysMatch-Game]

This video was very simple, but can you explain the need for using these determinant-type brackets
like (] or [)? I don’t know these yet 😳

[pierreneau]

I learnt: R+ means all x>=0. If x is different of 0, it's R+*. So solution should be [0, 4]