SOLUTION: Evaluate a^3 + 1/a^3 if a + 1/a = 6.

Algebra.Com
Question 1066053: Evaluate a^3 + 1/a^3 if a + 1/a = 6.
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
Evaluate a^3 + 1/a^3 if a + 1/a = 6.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Let   = 6.    (1)

Cube both sides of the equation (1). You will get

 +  +  +  =  =  216   (after using the formula for the cube of a sum  = ).

Now, cancel the factors  and . You will get

 +  +  +  = ,    or, after grouping the terms,

 +  +  = .

Replace  by 6, in accordance with the condition. You will get

 +  +  =     or

 +  =  -  =  = .

Thus    +  = .

Answer.    +  = .

See the lesson
    - HOW TO evaluate expressions involving  ,  ,    and  
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic "Evaluation, substitution".



Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Evaluate a^3 + 1/a^3 if a + 1/a = 6.
         			

 ------ Squaring the equation: 




 ------ Factoring 


6(34 - 1) ------- Substituting

RELATED QUESTIONS

Evaluate , if a = -3, and b =... (answered by JBarnum)
evaluate (a^4)^3 when a =... (answered by Alan3354)
Evaluate (a^4)^-3 when... (answered by stanbon)
helP! :) Evaluate : a^2 - ya - y(a-y) if y = -3 nad a =... (answered by stanbon)
Evaluate the expression. (a) (6) (3) (b) (10) (4) (3) (6) (2)... (answered by Alan3354)
Evaluate the expression, log 3^9 a. 1/2 b. 2 c. 6 d. 1 (answered by oscargut)
Evaluate: | -3 - 2 | - | 2 - 6 | a. 1; b; -9; c. -1; d. 9 (answered by jim_thompson5910)
Please help to : Evaluate a^2 - b^3(a - b) if a = 1/3 and b = -... (answered by tutorcecilia)
Evaluate: -/6... (answered by Alan3354)