if a + 1/5a = 1 then evaluate a³ + 1/125×a³ ?
Answers
Answer:
b><bodybgcolor="skyblue">
\begin{gathered} \small\bf \red{hey \: user \: here \: is \: ans} \\ \\ \huge \bf \blue{solution} \\ \\ \small \bf \pink{given \: that} \\ \\ \small \bf \pink{a + \frac{1}{5a} = 1} \\ \\ \small \bf \pink{we \: have \: to \: find \: the \: value \: of \: } \\ \small \bf \pink{ {a}^{3} + \frac{1}{125 {a}^{3} } } \\ \\ \small \bf \pink{let \: start} \\ \\ \small \bf \pink{as \: given} \\ \\ \small \bf \pink{a + \frac{1}{5a} = 1 \: \: \: equation \: 1st} \\ \\ \small \bf \blue{ \underline{cubing \: on \: both \: sides}} \\ \\ \small \bf \pink{ {(a + \frac{1}{5a} )}^{3} = {1}^{3} } \\ \\ \small \bf \red{ \huge \: now} \\ \\ \small \bf \orange{using \: to \: this \: identity} \\ \\ \small \bf \green{(a + b)^{3} = {a}^{3} + {b}^{3} + 3ab(a + b) } \\ \\ \small \bf \pink{ {a}^{3} + \frac{1}{125 {a}^{3} } + 3 \times a \times \frac{1}{5a}(a + \frac{1}{5a} ) = 1 } \\ \\ \small \bf \pink{ {a}^{3} + \frac{1}{125 {a}^{3} } + 3 \times \cancel{a} \times \frac{1}{5 \cancel{a}} \times ( 1) = 1} \\ \small \bf \pink{hence \: a + \frac{1}{5a} = 1(from \: equation \: 1st )} \\ \\ \small \bf \pink{ {a}^{3} + \frac{1}{125 {a}^{3} } + \frac{3}{5} = 1} \\ \\ \small \bf \pink{ {a}^{3} + \frac{1}{125 {a}^{3} } = 1 - \frac{3}{5} } \\ \\ \small \bf \pink{ {a}^{ 3} + \frac{1}{125 {a}^{3} } = \frac{5 - 3}{5} } \\ \\ \small \bf \pink{ {a}^{3} + \frac{1}{125 {a}^{3} } = \frac{2}{5} \: \: answer }\end{gathered}
heyuserhereisans
solution
giventhat
< marquee \: behavior = "alternate" > < marquee \: bgcolor = "red" > <marqueebehavior="alternate"><marqueebgcolor="red">
\begin{gathered} \bf \boxed{ \bf \blue {\: thanks \: for \: asking}} \\ \bf \purple{abdul \: is \: here} \\ \bf \green{ \huge \: follow \: me}\end{gathered}
thanksforasking
i hope it's help u❤
abdulishere
followme
i hope it's help u