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The sum of two digit number is 16 and the sum of their reciprocal is 1/3 . Find the numbers

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by Ajin

I want answer with expianation

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by Ajin

I want answer with expianation

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The Brainliest Answer!

Let the two numbers be x and y

Therefore x +y =16....(1)

Again

1/x +1/y =1/3

x+y/xy = 1/3 ⇒ xy=3*16

⇒ xy =48

⇒x = 48/y

On putting value of x in eq(1) we get

48/y +y =16

⇒48 + y² = 16 y

⇒y²- 16y + 48 = 0

⇒y²- 12y - 4y +48 =0

⇒ (y - 12) (y - 4) = 0

⇒ y = 12 or 4

Now for y = 12 ,x =16 - 12 =4

and for y = 4 ,x =16 - 4 = 12

so 12 and 4 are the answers.