1)
\\\textit{Find the values of }\left | a \right |+\left | b \right |\textit{such that the identity }\\ \left | ax+by \right |+\left | bx+ay \right |=\left | x \right |+\left | y \right |\emph{holds } \forall x ,y\epsilon R
2) \textit{find the smallest positive solution of the eq. } \sqrt{sin(1-x)}=\sqrt{cosx}
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1 Answers
11) |ax+by| <= |a||x| + |b||y|
|ay+bx| <= |a||y| + |b||x|
adding these two
|ax+by| + |ay+bx| <= (|a|+|b|)(|x|+|y|)
|x| + |y| <= (|a|+|b|)(|x|+|y|)
|a|+|b| >= 1
