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the sum of two numbers is 15 if their reciprocals is 3/10 find the two number using quadratic formula plz fast friends

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by aaa345

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by aaa345

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other no be =y

According to question

x+y=15⇒Y=15-x

1/X+1/Y=3/10

1/x+1/15-x=3/10

taking LCM

(15-X) X 10

150=45X-3X^2

3x^2-45x+150=0

x^2-15x+50=0

x^2 -10x-5x+50=0

x(x-10) -5(x-5)=0

(x-5) (x-10)=0

x=5 ,x=10

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Let the number be x

and second number be y

so given x + y = 15

and

⇒

⇒ {x + y = 15}

⇒

⇒

⇒ { x + y = 15 ⇒ y = 15 - x }

⇒

⇒

⇒

⇒

⇒

so x = 5 or 10

so when x = 10 then y = 15 - 10 = 5 so x = 10 , y = 5

and when x = 5 then y = 15 - 5 = 10 so x = 5 , y = 10

and second number be y

so given x + y = 15

and

⇒

⇒ {x + y = 15}

⇒

⇒

⇒ { x + y = 15 ⇒ y = 15 - x }

⇒

⇒

⇒

⇒

⇒

so x = 5 or 10

so when x = 10 then y = 15 - 10 = 5 so x = 10 , y = 5

and when x = 5 then y = 15 - 5 = 10 so x = 5 , y = 10