Let a, b and c be a real numbers such that a>0, b<0 and c<0. Find the sign of each expression. a) -b b) a+c c) c-a d) ab^2

Question
Let a, b and c be a real numbers such that a>0, b
a) -b
b) a+c
c) c-a
d) \(\displaystyle{a}{b}^{{2}}\)

Answers (1)

2020-11-09
(a) Here \(\displaystyle{b}{<}{0}\Rightarrow−{b}\)</span> will be a positive number.
Thus, sign of -a is positive.
(b) It is known that product of two negative number will be positive.
As \(\displaystyle{b}{<}{0}{\quad\text{and}\quad}{c}{<}{0}\Rightarrow{b}{c}{>}{0}.\)
Thus, sign of bc is positive.
So a and bc positive.
It is known that sum of two positive number will be positive.
Thus, a+bc>0.
Thus, sign of a + bc is positive.
(c) It is known that when a positive number is subtracted from a negative number, the resultant number will be negative .
Here \(\displaystyle{a}{>}{0},{c}{<}{0}\Rightarrow{c}−{a}{<}{0}\)</span>.
Thus, sign of a-b is negative .
(d) The square of ay number will be positive. Thus, \(\displaystyle{b}^{{2}}{>}{0}\) and given a>0.
Thus, \(\displaystyle{a}{b}^{{2}}{>}{0}\).
Therefore, the sign of \(\displaystyle{a}{b}^{{2}}\) is positive.
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