Question

if a2 +1/a2=7 find a3+1/a3​

Answer 1

Step-by-step explanation:

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Answer 2

given

a² + 1/a² =7

a² + 1/a² + 2 = 7+2 (adding 2 both sides)

(a + 1/a)² = 9

a + 1/a = ± 3

so a+1/a=3 -------(1)

and a+1/a= -3 -------(2)

Cubing both sides in equation (1) we get

( a+ 1/a)³ = 27

a³ + 1/a³ +3(a+1/a) = 27

a³ + 1/a³ +3×3 = 27 [ since a + 1/a =3]

a³ + 1/a³ =18

And cubing both sides equation (2)

(a+1/a)³ = -27

a³ + 1/a³ + 3(a+1/a) = -27

a³ + 1/a³ +3(-3) = -27 [since a+1/a= -3]

a³ + 1/a³ -9 = -27

a³ + 1/a³ = -27+9

a³ + 1/a³ = -18