Latest Elitmus Aptitude Question SOLUTION: If m^2-8m+1=0,then m^3+m^(-3)= ?

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(#M40152557) ELITMUS Numerical Ability question Equations Keep an EYE

If m^2-8m+1=0,then m^3+m^(-3)= ?

Asked In Elitmus Souradeep Guhathakurta (8 years ago)

Unsolved Read Solution (6)

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kumar saurav  (8 years ago)

here from equation 1 we will get
m^2-8m+1=0
m^2=8m-1
m=(8m-1)/m.........(1)
m=8-1/m
so m+1/m=8
now in equation 2
m^3+1/m^3
(m+1/m)(m^2 - m*1/m + 1/m^2)
(m+1/m)(m^2 - 1 + 1/m^2)
(m+1/m)(m^2 + 1/m^2 - 1)
(m+1/m){(m+1/m)^2 - 2m*1/m - 1} {since a^2+b^2=(a+b)^2-2ab}
(m+1/m){(m+1/m)^2 - 2-1}
now putting the value of m from equation 1
8(8^2-2-1)
8(64-3)
=488

Is this solution Helpfull? Yes (23) | No   

sudha singh  (8 years ago)

m^2-8m+1=0
Now , m^2=8m -1
Dividing both sides by m,we get
m =8 - (1/m)
So,
m^3 +1/m^3
=(m+1/m)(m^2 - 1 + 1/m^2) {bcoz a^3 +b^3= (a+b)(a^2 - ab + b^2)}
=8{(m+1/m)^2 - 4} As m+1/m =8 and [a2+b2 - 2ab=(a-b)2=(a+b)2-4ab)]
=8[8^2-4]
=8[64-4]
=480 Ans

Is this solution Helpfull? Yes (4) | No (2)  

Rishi Dev  (8 years ago)

ans:-488
m^3+m^-3
(m^6+1)/m^3
(m^2+1)(m^4+1-m^2)/m^3
(8m)(62m^2-m^2)/m^3 (m^2+1=8m from if condition and square both side then m^4+1=62 m^2)
8*61
488

Is this solution Helpfull? Yes (3) | No   

jitendra  (8 years ago)

m^2-8m+1=0
m say div
m+1/m=8 -1
m^3+m^(-3)= (m+1/m)^3 -3(m+1/m)
=(8)^3 - 3*8
=488

Is this solution Helpfull? Yes (1) | No   

mukesh kumar  (8 years ago)

m2-8m+1=0
first find value of m=(4+root(15),4-root(15))
m3+1/m3=(m+m)(m2-m2+m2)
= 2m(m2 )
=2m3
=2[4+root(15)]^3
After solving we get value of
m3+1/m3= 128+30root(15) Ans

Is this solution Helpfull? Yes | No (2)  

kundan prasad  (8 years ago)

Ans : 488

Is this solution Helpfull? Yes | No (1)  

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