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Megha Kumar

· started a discussion

· 1 Months ago

query (Question: 186117.0 )

please explain why are we takin a6+1=0

Question:
If a + \(\cfrac{1}{a}\)  = \(\sqrt{3}\), then the value of a18 + a12 + a6 + 1 is –
Options:
A) 0
B) 1
C) -1
D) 4
Solution:
Ans: (a)  

a18 + a12 + a6  + 1 

= a12 (a6 +1) + 1 (a6 + 1)

\(\therefore \)  

=  (a12 + 1) (a6 +1) 

= (a12 + 1) × 0 = 0 

Knowledge Expert

· commented

· 1 Months ago

Dear Student,
Please refer the below solution,
As a + 1/a = root 3
We know that ( a+ 1/a)^3 = a^3 + 1/a^3 + 3(a+1/a)
put value of a+ 1/a = root 3
we get ( root 3) ^3 = a^3 +1/ a^3 + 3(root3)
a^3 + 1/ a^3 = root 3 - root 3 = 0

As a^3 + 1/ a^3 = 0
Solve by taking lcm you get , a^6 1 = 0.
Now you can solve as given in the solution.


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