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m=2-(3)^(1/2) Find the value of (m^6+m^5+m^4+1)/m^3

m=2-(3)^(1/2)
Find the value of (m^6+m^5+m^4+1)/m^3

Grade:12th pass

7 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
9 years ago
Hello student,
Please find the answer to your question below
as m=2-\sqrt{3}
m2=7-4\sqrt{3}
m3=26-15\sqrt{3}
1/m3=26+15\sqrt{3}
Given (m6+m5+m4+1)/m3=m+m2+m3+1/m3
=2-\sqrt{3}+7-4\sqrt{3}+26-15\sqrt{3}+26+15\sqrt{3}
=61-5\sqrt{3}
Aditi
12 Points
9 years ago
Is there any shorter way to solve this?
i got this question in an aptitude test which had 30 questions for 30 minutes.. so i am supposed to solve this in like a minute or so.. 
 
Aditi
12 Points
9 years ago
is there any shorter way of solving this? 
 
Aditi
12 Points
9 years ago
is therr any shorter way of answering this?
mycroft holmes
272 Points
9 years ago
Wish I could post the solution, but this site has a primitive editor 
mycroft holmes
272 Points
9 years ago
m = 2 – 3^(1/2), and so m + 1/m = 4.
 
We can also write this last equation as m^2 = 4m-1
 
Given expression = (m^3+1/m^3) +m^2+m 
 
Now, using the identity: a+b+c = 0 implies a^3+b^3+c^3 = 3abc, we have
 
m + 1/m – 4 implies m^3 + 1/m^3 – 64 =  3 (m) (1/m) (-4) = -12 
 
so that m^3 + 1/m^3 = 64-12 = 52.
 
Also m^2+m = (4m-1)+m = 5m-1 = 9 – 5(2^1/2)
 
Adding up we get the given expressions equals 61 – 5 (2^1/2)
SHAIK AASIF AHAMED
askIITians Faculty 74 Points
9 years ago
Hello student,
This may help you
m = 2 – 3^(1/2), and rationalising this we get m + 1/m = 4. som^2 = 4m-1
Given equation is= (m^3+1/m^3) +m^2+m
From the identity if a+b+c = 0 gives a^3+b^3+c^3 = 3abc,
we havem + 1/m – 4=0 gives m^3 + 1/m^3 – 64 = 3 (m) (1/m) (-4) = -12
so m^3 + 1/m^3 = 64-12 = 52.
Also m^2+m = (4m-1)+m = 5m-1 = 9 – 5(3^1/2)
so m+m2+m3+1/m3=61 – 5 (3^1/2)

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