Question

When..a+1/a=1 ;a^3+1=?

Answer 1

Question :

$\sf \small If \: a + \frac{1}{a} = 1 \: then \: what \: is \:the \: value \: of \: {a}^{3} + \frac{1}{ {a}^{3} }$

To find :

$\sf \small \: the \: value \: of \: {a}^{3} + \frac{1}{ {a}^{3} }$

Formula Used :

$\underline{ \boxed{ \green{ \sf \small a^{3} + \frac{1}{ {a}^{3} } } \rarr \pink{(\sf \small a + \frac{1}{a} )^{3} } - \purple{\sf \small 3(a + \frac{1}{a} )}}}$

Solution :

$\sf \small a^{3} + \frac{1}{ {a}^{3} } (\sf \small a + \frac{1}{a} )^{3} - 3(a + \frac{1}{a} )$

Putting the value of a + 1/a we get

$\sf \small a^{3} + \frac{1}{ {a}^{3} } \rarr {(1)}^{3} - 3(1)$

$\sf \small a^{3} + \frac{1}{ {a}^{3} } \rarr1 + 3$

$\sf \small a^{3} + \frac{1}{ {a}^{3} } = 4$

Final Answer :

$\sf \small \: \therefore The \: value \: of \: a^{3} + \frac{1}{ {a}^{3} } is \: \underline{ \boxed{ 4 }}$

Answer 2

Step-by-step explanation:

$Putting the value of a + 1/a we get</p><p></p><p>\sf \small a^{3} + \frac{1}{ {a}^{3} } \rarr {(1)}^{3} - 3(1)a </p><p>3</p><p> + </p><p>a </p><p>3</p><p> </p><p>1</p><p> </p><p> →(1) </p><p>3</p><p> −3(1)</p><p></p><p>\sf \small a^{3} + \frac{1}{ {a}^{3} } \rarr1 + 3a </p><p>3</p><p> + </p><p>a </p><p>3</p><p> </p><p>1</p><p> </p><p> →1+3</p><p></p><p>\sf \small a^{3} + \frac{1}{ {a}^{3} } = 4a </p><p>3</p><p> + </p><p>a </p><p>3</p><p> </p><p>1</p><p> </p><p> =4$