Question

the sum of two numbers is 15.if the sum of their reciprocals is 3/10 . Find thr numbers​

Answer 1

Step-by-step explanation:

let the 1st number to be =x

then second number = 15-x

now sum of their reciprocal is 3/10

acc to ques?

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

15-x-x/ 15-x^2= 3/10

10×(15-2x)= 3×(15x-x^2)

150-20x= 45x- 3x^2

3x^2-65x+150

3x^2-75x+10x+ 150

3x(x-15) -10(x-15)

(3x-10) (x-15)

x= 15 and another is x=10/3

i hope it will help u

mark me in brainlist

Answer 2

$\bf{\underline{Given}}\gray{{:-}}$

• The sum of two numbers is 15.

• And sum of their reciprocal is 3/10

$\bf{\underline{To\:Find}}\gray{{:-}}$

• The required number = ?

$\bf{\underline{Solution}}\gray{{:-}}$

Let the required number be x and (15 - x)

Then,

$\rm\dfrac{1}{x}+\dfrac{1}{(15-x)}=\dfrac{3}{10}$

$\rm\longrightarrow\dfrac{(15-x)+x}{x(15-x)}=\dfrac{3}{10}$

$\rm\longrightarrow\dfrac{15}{x(15-x)}=\dfrac{3}{10}$

⚫ By cross multiplication :-

$\rm\longrightarrow\:3x(15-x)=150$

$\rm\longrightarrow\:45x-3{x}^{2}=150$

$\rm\longrightarrow\:3{x}^{2}-45x+150=0$

$\rm\longrightarrow\:3({x}^{2}-15x+50)=0$

$\rm\longrightarrow\:{x}^{2}-15x+50=0$

$\rm\longrightarrow\:{x}^{2}-10x-5x+50=0$

$\rm\longrightarrow\:x(x-10)-5(x-10)=0$

$\bf\longrightarrow\:(x-10)(x-5)=0$

Now,

$\rm\:x-10=0$

$\rm\longrightarrow\:x=0+10$

$\bf\longrightarrow\:x=10$

Then,

$\rm\:x-5=0$

$\rm\longrightarrow\:x=0+5$

$\bf\longrightarrow\:x=5$

Hence,the required number will be 5 and 10.