Latest Campus Aptitude Question SOLUTION: If 1/x+x=5 and find out the value x^5+1/x^5=?

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(#M40034495) CAMPUS Numerical Ability question Keep an EYE

If 1/x+x=5 and find out the value x^5+1/x^5=?

Asked In Campus moumitabhakat (10 years ago)

Solved Saraswathy Read Solution (5)

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Read Solution (5) :

Saraswathy  (10 years ago)

x + 1/x = 5

first calculate (x + (1/x))^2
(x + (1/x))^2 = 5^2
x^2 + (1/x)^2 + 2 = 25
x^2 + 1/x^2 = 23 ---->(1)


Now calculate (x + (1/x))^3
(x + 1/x)^3 = 5^3
x^3 + y^3 +3x*1/x(x + 1/x) = 125
x^3 + y^3 + 15 = 125
x^3 + y^3 = 110 --->(2)

Multiply (1) & (2)
(x^2 + 1/x^2)(x^3 + 1/x^3) = 23 * 110
x^5 + 1/x + x + 1/x^5 = 2530
x^5 + 1/x^5 + 5 = 2350
x^5 + 1/x^5 = 2345

Ans : 2345

Is this solution Helpfull? Yes (6) | No (3)  

Ahalya.A  (10 years ago)

I think that ans is 2525..... the procedure is right but when subtracting 2530 by 5 we get 2525..............

Is this solution Helpfull? Yes (4) | No   

Saraswathy  (10 years ago)

Ya @Ahalya ... Its 2525...

Is this solution Helpfull? Yes (1) | No   

anusha  (10 years ago)

ans=100001
1/2x=5
10x=1
x=1/10
[x^5(1+1/x^5)]/x^5=1+100000=100001

Is this solution Helpfull? Yes | No (4)  

RAKESH  (10 years ago)

x^2 + 1/x^2 = (x+ 1/x)^2 - 2 = 5^2 - 2 = 23 -------(1)

x^3 + 1/x^3 = (x+ 1/x)^3 - 3*x*1/x*(x+ 1/x) = 5^3 - 3*5 = 110 -------(2)

multiplying (1)& (2)

=>(x^2+ 1/x^2)*(x^3+ 1/x^3) = 23*110
=> x^5 + 1/x + x + 1/x^5 = 2530
=> x^5 + 1/x^5 + (x+ 1/x)= 2530
=> x^5 + 1/x^5 + 5 = 2530
=> (x^5+ 1/x^5)= 2345

Is this solution Helpfull? Yes | No (3)  

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