- #1

utkarshakash

Gold Member

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## Homework Statement

For a,b belongs to R the maximum value of [itex](a-1)(b-1)+(1-\sqrt{1-a^2})(1-\sqrt{1-b^2})[/itex]

## Homework Equations

## The Attempt at a Solution

I'm really clueless regarding how to start. So I started putting some arbitrary values but they were of no help. I can't even differentiate it as it is not a function in one variable. But it is clear that whatever value a and b attains, the following inequalities must be satisfied.

1-a^2>0

1-b^2>0

This means that a and b must lie between -1 and 1. So far I could shorten the range of a and b. I also remember that I posted a very similar question earlier and someone suggested me to use geometric methods rather than solving it algebraically. OK, so I assume a function [itex]y=\sqrt{1-x^2}[/itex]. Now by inspection the original function transforms to [itex](x_1 - 1 )(x_2 - 1) + (1-y_1)(1-y_2)[/itex].

But I really don't know how this helps me.

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