Math, asked by adityasingh2692006, 8 months ago

Verify that |a+b| <_ |a| + |b| .Take a=1/3 , b = -2/9

Answers

Answered by naavyya
1

Step-by-step explanation:

a + b = \frac{1}{3} + \frac{-2}{9} = \frac{(3*3) - 2}{9} = \frac{9-2}{9} = \frac{7}{9}

LHS = |a+b| = | \frac{7}{9}| =  \frac{7}{9}

|a| = |\frac{1}{3} | =  \frac{1}{3}    and  |b| =  | \frac{-2}{9}| =  \frac{2}{9}

RHS = |a| + |b| =  \frac{1}{3} + \frac{2}{9} =  \frac{(3*3) + 2}{9} =  \frac{9+2}{9} = \frac{11}{9}

\frac{7}{9} <  \frac{11}{9}

|a+b| < |a| + |b|

Hence proved.

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