The sum of two number is 15 .if the sum of their recipocals is 3/10 find the number.

Solution: Let the required number be x and 15 -x then,

$\\ 1/x+1/15-x=3/10 \\ \\\Rightarrow 15-x+x/x(15-x)=3/10\\ \\\Rightarrow 15/x(15-x)=3/10\\ \\\Rightarrow 150=3x(15-x)\\ \\\Rightarrow 150=45x-3x^2$

$\\ x^2-15x+50=0\\ \\\Rightarrow (x-10)(x-5)=0\\ \\\Rightarrow x=10;or ;x=5$

Hence ,the two number are 10 and 5

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