Latest Mu Sigma Aptitude Question SOLUTION: If m^2+m^-2=23;then what is the value of m^3+m^-3?

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If m^2+m^-2=23;then what is the value of m^3+m^-3?

Asked In Mu Sigma Arun Prakash (9 years ago)

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RAKESH  (9 years ago)

m^2+m^-2=23
=> (m + m^-1)^2 - 2 = 23
=> (m + m^-1) = 5

m^3+m^-3 = (m + m^-1)^3 - 3(m + m^-1) = 5^3 - 3*5 = 110

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tirupathi reddy  (9 years ago)

Ans:110

m^2+(1/m^2)=23

m+1/m=?

By solving. (m+1/m)^2 =m^2 + 1/m^2 + 2

We get m + 1/m = 5

Use a^3+b^3 formula by keeping a=m, b=1/m

m^3+1/m^3=(m+1/m)(m^2-m(1/m)+1/m^2)

=5 (23-1)

=110.

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meenaravi  (9 years ago)

here m2+m-2=23 can be written as m2+1/m2=23
(it can be also written as in the format of (a+b)2=a2+b2=2ab))
m2+1/m2+2(m)(1/m)=m2+1/m2+2=(m+1/m)2
so (m+1/m)2=23+2(because m2+1/m2=23)
m+1/m=5
(a3+b3=(a+b)(a2-ab+b2))
m^3+1/m^3=(m+1/m)(m^2-m(1/m)+1/m^2)

=5 (23-1)

=110.

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