Latest SSC Aptitude Question SOLUTION: x^2-3x+1=0 then X^5+1/X^5

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(#M40029914) SSC Numerical Ability question algebra Keep an EYE

x^2-3x+1=0

then

X^5+1/X^5

Asked In SSC prabhat kumar (10 years ago)

Solved prabhat kumar Read Solution (3)

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Read Solution (3) :

prabhat kumar  (10 years ago)

x*x=3x-1
or x=3-1/x
or x+1/x=3

(x+1/x)^2=9
x^2+1/X^2=7

(x+1/x)^3=27
X^3+1/x^3=18
(x^2+1/x^2)(x^3+1/X^3)=126
x^5+1/x^5=126-3=132

Is this solution Helpfull? Yes (12) | No (2)  

abhi  (10 years ago)

x^2-3x-1=0 then we find x
by quadratic sol.
(x-2)(x-1)
x=1,2
then
put either 1 or 2 according to the options ans
by 1
1^5+1/1^5=2
by 2
2^5+1/2^5=32+1/32=32.03125

Is this solution Helpfull? Yes (3) | No (13)  

Krishanu Bhattacharya  (10 years ago)

x^2-3x+1=0 =>x-3+1/x=0 =>x+1/x=3....(i)
Now, x^5+1/x^5=(x+1/x)(x^4+x^3.1/x+x^2.1/x^2+x.1/x^3+1/x^4)
putting (i) in here we get,
3.(x^4+1/x^4+1+1/x^2)
= 3.[((x+1/x)(x^3+x^2.1/x+x^2.1/x+x.1/x^2+1/x^3)
=3.3.3(x^2+1/x.x+1/x^2)
=3.3.3[(x+1/x)^2-2.x.1/x]
=3.3.3.[3^2-2]
=27.7
=189 (ans)

Is this solution Helpfull? Yes | No (2)  

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