Question

the sum of 2 num is 2 and the sum of their reciprocals is 2.25 find the numbers​

Answer 1

Let the numbers be x and y .

Given x+y=2 -(1)

Also 1x+1y=2.25 (this clearly rules out x=0,y=0 )

∴x+y=2.25xy

∴2=94x(2−x)

∴9x2−18x+8=0 -(2)

Solving equation (2),

D=(−18)2−4(9)(8)=36>0 Hence two unique solutions

x=−(−18)±36√2×9

∴x=43 or x=23

∴y=23 or y=43

Thus the solution is (43,23) .

Hope it helps!