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Mannu Kumar Singh

· started a discussion

· 1 Months ago

did not understand (Question: 186117.0 )

how did you get the value of a^6+1... make it more clear

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

Given that: (a + 1/a) = √3
Apply the the formula, (a^3 + b^3) = (a + b)^3 - 3ab(a + b)
Therefore, (a^3 + (1/a)^3) = (a + 1/a)^3 - 3 x a x 1/a (a + 1/a)
Put a+1/a=√3
So, (a^3 + (1/a)^3) = (√3)^3 - 3(√3) = 3√3 - 3√3 = 0
Take lcm, (a^6+1)/a^3=0, so, a^6+1=0
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