if a + 1/5a = 1 then evaluate a³ + 1/125×a³ ?
Answers
Step-by-step explanation:
Given :-
This relation is given
To find:
Solve as follows:
By using identity
Put in the values:
Put the value from relation:
Answer:
Given :-
This relation is given
a + \frac{1}{5a} = 1a+
5a
1
=1
To find:
\begin{gathered}\begin{lgathered}{a}^{3} + \frac{1}{125 {a}^{3} } \\\end{lgathered} \end{gathered}
Solve as follows:
By using identity
\begin{gathered}\begin{lgathered}{(a + b)}^{3} = {a}^{3} + {b}^{3} + 3ab(a+b) \\ \\\end{lgathered} \end{gathered}
Put in the values:
\begin{gathered}\begin{lgathered}{a}^{3} + \frac{1}{125 {a}^{3} } = {(a + \frac{1}{5a} )}^{3} - 3a\frac{1}{5a}(a + \frac{1}{5a} ) \\ \\\end{lgathered} \end{gathered}
Put the value from relation:
\begin{gathered}\begin{lgathered}{a}^{3} + \frac{1}{125 {a}^{3} } = {1}^{3} - 3\frac{1}{5}(1) \\ \\ = 1 + \frac{3 }{5}\\ \\ = - \frac{2}{5}\end{lgathered} \end{gathered}