Question

if x+y=9 & 1÷x+1÷y=2 find the value of x&y

Answer 1

x+y=9
So, y=9-x -------------- (1)

1/x+1/y=2

From equation (1), we get,
1/x + 1/(9-x) = 2
(9-x+ x)/ [x(9-x)] = 2
9/9x-x^2 = 2
2(9x-x^2) = 9
18x - 2x^2-9=0
2x^2-18x+9=0
Comparing with,
ax^2+bx+c=0

a=2, b=-18, c=9

Using the quadratic formula,

x= [-b +/- √b^2 - 4ac]/2a
x= [-(-18) +/- √(-18)^2 - 4(2)(9)]/ 2(2)
x = (18 +/- √324 -72)/ 4
x = (18+/- √252)/4
x = (18 +/- 6√7)/4
x = (18 +/- 6*2.645)/4
x = (18 +/- 15.87)/4
x = (18+ 15.87)/4 , (18- 15.87)/4
x = 33.87/4 , 2.13/4
x = 8.467 , 0.5325
x = 8.5 , 0.5

When, x= 8.5, y = 0.5
When, x= 0.5, y = 8.5