Math, asked by funnybones95, 7 months ago



QUADRIC EQUATION

The sum of two numbers is 60 & the sum of their reciprocal is 3/40. Determine the numbers​

Answers

Answered by snehitha2
0

Answer:

20 and 40

Step-by-step explanation:

  Let the two numbers be "x" and "y"

According to the question :

 x + y = 60

1/x + 1/y = 3/40

------------------------

\frac{1}{x} + \frac{1}{y}=\frac{3}{40} \\\\ \frac{x+y}{xy} =\frac{3}{40} \\\\ \frac{60}{xy} =\frac{3}{40} \\\\ xy=60 \times \frac{40}{3} \\\\ xy=800 \\\\ x=\frac{800}{y}

=> x + y = 60

   \frac{800}{y} +y=60 \\\\ \frac{800+y^2}{y} =60 \\\\ 800+y^2=60y \\\\ y^2-60y+800=0\\\\ y^2-40y-20y+800=0 \\\\y(y-40) -20(y-40)=0 \\\\ (y-40)(y-20) = 0 \\\\ y=20,40

If y = 20, x = 40

If y = 40, x = 20

The numbers are 20 and 40

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