Question

X+Y=8 and 1/x +1/Y=8/15

Answer 1

x + y = 8.
x = 8 - y.
Put this value in second equation.
1/x + 1/y = 8/15.
1/8-y + 1/y = 8/15.
8/8y-y^2 = 8/15.
15 = 8y - y^2.
y^2 -8y + 15 = 0.
y^2 - 5y - 3y + 15 = 0.
y( y - 5) -3 (y - 5) = 0
(y - 5)( y - 3 ) = 0 .
y = 5 , 3.
x = 8 - y.
x = 8-5 , 8-3.
x = 3 , 5.
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Answer 2

{X+Y=8} …….…(1)

1/x +1/Y=8/15
X+Y/XY=8/15
8/XY=8/15
{XY=15}. ………..(2)

Y=15/X (PUT IN ..1 )
X+ 15/X=8
X^2+15=8X
X^2–8X+15=0
(X–3)(X–5)=0

WHEN, X=3
Y=5

WHEN, X=5
Y=3.

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