Question

$Evaluate open vertical bar table row cell straight x plus straight lambda end cell straight x straight x row straight x cell space space straight x plus straight lambda end cell straight x row straight x straight x cell space space straight x plus straight lambda end cell end table close vertical bar$

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Solution

Let space space increment space equals open vertical bar table row cell straight x plus straight lambda end cell straight x straight x row straight x cell space space straight x plus straight lambda end cell straight x row straight x straight x cell space space straight x plus straight lambda end cell end table close vertical bar space space space space space space space space space space space space space equals space open vertical bar table row cell 3 straight x plus straight lambda end cell cell space space space 3 straight x plus straight lambda end cell cell space space space 3 straight x plus straight lambda end cell row straight x cell straight x plus straight lambda end cell straight x row straight x straight x cell bold x bold plus bold lambda end cell end table close vertical bar space space comma space by space straight R subscript 1 space plus straight R subscript 2 space plus straight R subscript 3 space space space space space space space space space space space equals space left parenthesis 3 straight x plus straight lambda right parenthesis space open vertical bar table row 1 1 1 row straight x cell space space straight x plus straight lambda end cell straight x row straight x straight x cell space space space straight x plus straight lambda end cell end table close vertical bar space space space space space space space space space space space space equals space left parenthesis 3 straight x plus straight lambda right parenthesis space open vertical bar table row 1 cell space space space space 0 space space end cell cell space space space 0 end cell row straight x cell space space straight lambda end cell cell space space 0 end cell row straight x cell space space 0 end cell cell space space straight lambda end cell end table close vertical bar space space by space straight C subscript 1 minus straight C subscript 2 space comma space straight C subscript 3 space minus straight C subscript 1 space space space space space space space space space space space equals space left parenthesis 3 straight x plus straight lambda right parenthesis space space open square brackets table row cell left parenthesis 1 right parenthesis left parenthesis straight lambda right parenthesis left parenthesis straight lambda right parenthesis end cell end table close square brackets space space space space space space space space space space space equals space straight lambda squared space left parenthesis 3 straight x plus straight lambda right parenthesis

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