Question

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

Answer 1

let the no be =x
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 =3
 (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

Answer 2

Let the number be x 
and second number be y

so given x + y = 15 
and  $\frac{1}{x}+\frac{1}{y}=\frac{3}{10}$

⇒$\frac{x+y}{xy}=\frac{3}{10}$

⇒$\frac{x+y}{xy}=\frac{3}{10}$     {x +  y = 15}

⇒$\frac{15}{xy}=\frac{3}{10}$

⇒$\50=xy$

⇒$50=x(15-x)$          { x + y = 15 ⇒ y = 15 - x }

⇒$50=15x - x^2$

⇒$x^2-15x+50=0$

⇒$x^2-10x-5x+50=0$

⇒$x(x-10)-5(x-10)=0$

⇒$(x-5)(x-10)=0$

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