The sum of two numbers is 15 . if the sum of their recipocal is 3/10 . Then find the numbre
Answers
x+y=15
1/x+1/y= 3/10
(y+x)/xy= 3/10
(x+y)=3/10xy
(15)×10/3 =xy
5×10=xy
50/y=x
50=x(15-x)
50=15x-x²
x²-15x+50=0
x²-10x-5x+50=0
x(x-10)-5(x-10)=0
(x-10)(x-5)=0
x=10,5
x be 10 & y be 5 vice -a - versa
Let the two numbers be x and y.
Given that sum of two numbers is 15.
= > x + y = 15 ------ (1)
Given that sum of their reciprocals is 3/10.
= > 1/x + 1/y = 3/10
= > (x + y)/xy = 3/10
= > 15/xy = 3/10
= > 150 = 3xy
= > xy = 50.
= > x = 50/y ----- (2)
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Substitute (2) in (1), we get
= > (50/y) + y = 15
= > 50 + y^2 = 15y
= > y^2 - 15y + 50 = 0
= > y^2 - 10y - 5y + 50 = 0
= > y(y - 10) - 5(y - 10) = 0
= > (y - 5)(y - 10) = 0
= > y = 5, 10.
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Substitute y = 5 in (1), we get
= > x + y = 15
= > x + 5 = 15
= > x = 10.
Substitute y = 10 in (1), we get
= > x + y = 15
= > x + 10 = 15
= > x = 5.
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Therefore,
The value of x = 5 (or) 10.
The value of y = 5 (or) 10.
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Hope this helps!