Find the value

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}

1 Answers

1
b_k_dubey ·

1) |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

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