Question

if(a+1/a)^2=9 then a^3+1/a^3 equals​

Answer 1

Answer:

if (a+1/a)^2 is 9 then a+1/a is 3

so, (a+1/a)^3 is 18

Answer 2

Answer:

18

Step-by-step explanation:

Concept= Algebra

Given= The value of an expression

To find= The value of another expression

Explanation=

We are given that if(a+1/a)²2=9 then a³+1/a³ equals​ what.

So we ultimately need to find the value of a³ + 1/a³.

Given that (a+1/a)²=9

So we take square roots both side

√(a+1/a)²=√9

(a+1/a)=3.

Now according the formula of (x + y)³ we know that,

(x + y)³ = x³ + y³ + 3xy(x + y)

Now applying the same concept to (a+1/a),

(a+1/a)=3

cubing both sides

(a+1/a)³ = 3³

a³ + 1/a³ + 3*a*1/a(a+1/a) = 27

a³ + 1/a³ + 3*(a+1/a) =27

Now we know that (a+1/a)=3, substituting this value we get,

a³ + 1/a³ + 3*3=27

a³ + 1/a³ +9=27

a³ + 1/a³ = 27-9

a³ + 1/a³ = 18

Hence we required the value of a³ + 1/a³ which is 18.

Therefore a³ + 1/a³ equals 18.

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