6. By taking a = 2/5 and b=-3/10, verify the following:
(i) |a+b| <|al +| b| (i) lab|=lal.|b|
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Answer:
Given,
\begin{gathered}a = \frac{2}{5} \\ b = \frac{ - 3}{10} \end{gathered}
a=
5
2
b=
10
−3
Now,
LHS,
\begin{gathered}|ab| \\ =|( \frac{2}{5})( \frac{ - 3}{10}) | \\ = | \frac{ - 6}{50} | \\ = \frac{6}{50} \\ = \frac{3}{25} \end{gathered}
∣ab∣
=∣(
5
2
)(
10
−3
)∣
=∣
50
−6
∣
=
50
6
=
25
3
And RHS,
\begin{gathered} |a| . |b| \\ = | \frac{2}{5} |. | \frac{ - 3}{10} | \\ = \frac{2}{5} \times \frac{3}{10} \\ = \frac{6}{50} \\ = \frac{3}{25} \end{gathered}
∣a∣.∣b∣
=∣
5
2
∣.∣
10
−3
∣
=
5
2
×
10
3
=
50
6
=
25
3
therefore,
LHS = RHS
Hence verified.
.
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