Latest IBM Aptitude Question SOLUTION: Solve for x and y: 1/x - 1/y = 1/3, 1/x2 + 1/y2 = 5/9.

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Solve for x and y:
1/x - 1/y = 1/3, 1/x2 + 1/y2 = 5/9.

Asked In IBM (12 years ago)

Unsolved Read Solution (3)

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Read Solution (3) :

Dr.Dipin Singh  (12 years ago)

X= 3/2 and Y = 3
1/x - 1/y = 1/3, 1/x^2 + 1/y^2 = 5/9.
squaring both sides of 1/x - 1/y = 1/3 and substituting value of 1/x2 + 1/y2 = 5/9, we get 2/xy = 4/9.

Find value of 1/x+1/y using formula (1/x+1/y)^2=(1/x - 1/y )^2 +4/xy
Then
1/x +1/y =1

solving these , we get
x= 3/2 and Y= 3

Is this solution Helpfull? Yes (9) | No (3)  

uthra murugesan  (8 years ago)

x = 3/2 or -3 and y = 3 or -3/2.


take 1/x=a, 1/y=b so, a-b=1/3, a2+b2=5/9, a2+b2=(a-b)2+2ab so, (a-b)2+2ab=5/9 (1/3)2+2ab=5/9 it gives ab=2/9 a=2/9b, so 2/9b-b=1/3 from this b=1/3 hence a=2/3 so x=3/2, y=3

Is this solution Helpfull? Yes (3) | No   

chandravardhan  (9 years ago)

(a-b)^2 = a^2+b^2-2ab

(1/x-1/y)^2= 1/x^2+1/y^2-2/xy

we know 1/x^2+1/y^2 =5/9


taking square root on both sides

(1/x-1/y)^2 = (1/3)^2

now you can simplify

Is this solution Helpfull? Yes | No (1)  

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