Question

the sum of two numbers is 15 sum of their reciprocal is 3 by that​

Answer 1

Let the two numbers be x and y respectively

Now,

According to the condition in the question,

x+y=15

→y=15-x

Also,

$\sf{ \frac{1}{x} + \frac{1}{y} = 3 }$

Putting y=15-x in the above equation,

$\sf{ \frac{1}{x} + \frac{1}{15 - x} = 3 } \\ \\ \implies \: \sf{ \frac{15 - x + x}{x(15 - x)} = 3} \\ \\ \implies \: \sf{15 = 45x - 3x {}^{2} } \\ \\ \implies \: \sf{3x {}^{2} - 45x + 15 = 0 } \\ \\ \implies \: \sf{x {}^{2} - 15x + 5 = 0 }$

On comparing with ax²+bx+c=0,

a=1,b= -15 and c=5

•Discriminant,D

b²-4ac

=(-15)²-4(1)(5)

=225-20

=195

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Now,

$\sf{x = \frac{ - b \pm \sqrt{d} }{2a} } \\ \\ \implies \: \sf{x = \frac{15 \pm \sqrt{195} }{2} }$