Question

if the value of a+1/a=14 then find the value of a^3+1/a^3 =?​

Answer 1

a + 1/a = 14

$( {x}^{3} + {y}^{3} = ( {x + y)}^{3} - 3xy(x + y))$

${a}^{3} + \frac{1}{ {a}^{3} } = ( {a + \frac{1}{a}) }^{3} -3 \times a \times \frac{1}{a} (a + \frac{1}{a} )$

$= {14}^{3} - (3 \times 14)$

$= 2744 - 42 = 2702$

Therefore, 2702 is the answer.

Answer 2

Step-by-step explanation:

a+1/a=14

a^3+1/a^3

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

=(a+1/a)^3 -3×a×1/a(a+1/a)

=(14)^3 -3×14

=2744-42

=2702