Question

Find two parts of 15 such that the sum of their reciprocals 3/10​

Answer 1

Step-by-step explanation:

I hope it will be help full for you

Answer 2

ANSWER:

Given:

• 2 parts of 15.
• Sum of reciprocals is 3/10.

To Find:

• The parts.

Solution:

$\text{Let one part of 15 be x.}\\\\\text{So, the other part will be (15 - x).}\\\\\text{Hence,}\\\\:\implies\text{Reciprocal of x =} \dfrac{1}{x}\\\\:\implies\text{Reciprocal of (15 - x) =} \dfrac{1}{15 - x}}\\\\\text{So,}\\\\:\implies \dfrac{1}{x}+\dfrac{1}{15-x}=\dfrac{3}{10}\\\\\text{Taking LCM,}\\\\:\implies\dfrac{15-x+x}{(x)(15-x)}=\dfrac{3}{10}\\\\:\implies\dfrac{15}{15x-x^2}=\dfrac{3}{10}\\\\\text{On cross multiplying,}\\\\:\implies15\times10=3\times(15x-x^2)\\\\:\implies150=45x-3x^2$

$:\implies3x^2-45x+150=0\\\\:\implies3(x^2-15x+50)=0\\\\:\implies x^2-15x+50=0\\\\\text{On splitting the middle term,}\\\\:\implies x^2-10x-5x+50=0\\\\:\implies x(x-10)-5(x-10)=0\\\\:\implies(x-10)(x-5)=0\\\\\text{So,}\\\\\bf{:\implies x=10\:\:\:or\:\:\:x=5}\\\\\text{So,}$

$:\implies 15-x=15-5\:\:\:or\:\:\:15-10\\\\\bf{:\implies15-x=10\:\:\:or\:\:\:5}\\\\\text{\bf\underline{Hence, the numbers are 10 and 5.}}}$