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Expert: Pawan Musale - 9/28/2009


Question
if a + 1/a=3 then the value of a3 + 1/a3(this is a's cube)=

Answer
Deepika,

a+1/a = 3 ------------------ #1

Let us make cube on both sides

(a+1/a)^3 = 3^3 ----------- #2

Now we will use following expansion formula:

(a+b)^3 = a^3 + b^3 + 3a^2b + 3ab^2

Applying this formula to #2 above,

a^3 + 1/a^3 + 3a^2*(1/a) + 3a*(1/a^2) = 27

a^3 + 1/a^3 + 3a + 3*(1/a) = 27

a^3 + 1/a^3 + 3(a + 1/a) = 27  ..... (taking out 3 as common multiplier)

Now we know that a+1/a = 3. So putting this in above equation,

a^3 + 1/a^3 + 3(3) = 27

a^3 + 1/a^3 + 9 = 27

a^3 + 1/a^3 = 18

I believe this helps you. Kindly let me know if you need additional information on this.

All the best for your studies. :)

Regards,
Pawan  

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Pawan Musale

Expertise

I can answer Basic Mathematics questions like: Natural Numbers, Integers, Real Numbers, Complex Numbers, Number Theory, Geometry, Trigonometry, Graph Theory, Square Roots, Basic Integration, Profit-Loss problems, Work-Time problems, Equations etc I can try to answer questions of probability and set theory

Experience

Tutoring on allexperts.com since long time

Education/Credentials
I am Bachelor of Engineering (Instrumentation) from the reputed institute in India.

Awards and Honors
I was 18th in High School Scholarship examination in Maharashtra State of India. I was second in Mathematics in Maharashtra State in Secondary School Certificate examination.

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