Question

a+1/a =7 ,find the value of a^3 +1/a^3

Answer 1

Given,
A+1/a=7
Since (a+b)³=a³+b³+3ab(a+b)
(A+1/a)³=a³+1/a³+3(a×1/a)(a+1/a)
Putting value
7³=a³+1/a³+3×7
343=a³+1/a³+21
343-21=a³+1/a³
322=a³+1/a³
(ÆÑẞWĒR)

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Answer 2

$\textbf{Answer}$

We are given the value,
$\textbf{a + 1/a = 7}$

$\textbf{We need to find the value of,}$
a^3 + 1/a^3 = ?

$\textbf{We know the formula,}$

(a + b)^3 = a^3 + b^3 + 3ab(a + b)

$\textbf{Lets get back to the given value,}$

(a + 1/a) = 7
=> (a + 1/a)^3 = a^3 + 1/a^3 + 3(a).(1/a).(a + 1/a)

$\textbf{Putting (a + 1/a) = 7,}$

=> 7^3 = (a^3 + 1/a^3) + 3(7)

=> (a^3 + b^3) = (7×7×7) - (3×7)

=> (a^3 + b^3) = 343 - 21

=> (a^3 + b^3) = 322

$\textbf{Hence the value of}$(a^3 + 1/a^3) $\textbf{is 322.}$

$\textbf{Hope My Answer Helped}$

$\textbf{Thanks}$