Question

the sum of two number is 15 if the sum of the reciprocal is 3 by 10 find the number​

Answer 1

Let the nos be x nd (15-x)

thn

ATQ......

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

=> ( 15 - x + x ) / x (15-x) = 3 / 10

=> 15 / 15x - x² = 3 / 10

=> 5 / 15x - x² = 1 / 10

=> 50 = 15x - x²

=> x² - 15x + 50 = 0

=> x² - 10x - 5x + 50 = 0

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

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

hence the nos are 5 nd 10

hope it's helpful to uhh.......!!!!

Answer 2

$\huge \sf \color{purple}{\underline{\underline{Answer}}} :$

Two numbers are 5 and 10

$\huge \sf \color{purple}{\underline{\underline{Solution}}}:$

✯ Let the number be x .

✯ Then the other number is 15 - x.

$\sf \color{brown}{Using \: the \: given \: information \: , we\: get }$

$\sf \frac{1}{x}+\frac{1}{15-x}=\frac{3}{10} \\ \\ \sf \frac{15-x+x}{x(15-x)}=\frac{3}{10} \\ \\ \sf \frac{15}{(15x-x²)}=\frac{3}{10} \\ \\ \sf 150=45x-3x² \\ \\ \sf 3(x²-15+50)=0 \\\\ \sf x²-15+50=0 \\ \\ \sf x²-5x-10x+50 =0 \\ \\ \sf (x-10)(x-5)=0 \\ \\ \sf x-10=0 \: \: \ \ \ OR \ \ \ \ \sf x-5 \\ \\ \sf \boxed{ \colorbox{lightgreen}{x=10}} \ \ \ \ or \ \ \ \ \boxed{\colorbox{lightgreen}{ x = 5 }}$

$\color{red}━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━$

When x = 10 , then the other number is 15-5 = 10

When x = 5, then the other number is 15-5 = 10

$\color{red}━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━$

$\sf \color{blue}{Hence, \ the \ two \ numbers \ are \ 5 \ and \ 10 }$

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