Question

Sum of two number is 25 and product is 25.find two numbers

Answer 1

Answer:

Step-by-step explanation:

sum=25

let one no.=x

other no.25-x

product=25

(x*25-x)=25

x^2-25x=25

x^2-25x-25=0

Answer 2

Answer:

$value \: of \: a \: = \: \frac{10}{(5 + \sqrt{21)} } \\ \\ value \: of \: b = \frac{5(5 + \sqrt{21)} }{2}$

Step-by-step explanation:

$sum \: of \: two \: number \: is = 25 \\ product \: of \: two \: number = 25 \\ let \: the \: number \: be \: = a \: and \: b \\ a + b = 25.........(1) \\ ab = 25......(2) \\ from \: second \: equation \: we \: get \\ a = \frac{25}{b} \\ put \: this \: value \: in \: equation \: (1) \\ \frac{25}{b} + b = 25 \\ \frac{25 + {b}^{2} }{b} = 25 \\ 25 + {b}^{2} = 25b \\ {b}^{2} - 25b + 25 = 0 \\ d = {b}^{2} - 4ac = 0 \\ ( - 25) {}^{2} - 4(1)(25) = 0 \\ 625 - 100 = 0 \\ 525 = d \\ x = \frac{ - b + \sqrt{d} }{2a} \\ x = \frac{ - ( - 25) + \sqrt{525} }{2} \\ x = \frac{25 + 5 \sqrt{21} }{2} \\ \frac{5(5 + \sqrt{21)} }{2} = b \\ put \: the \: value \: of \: b \: in \: equation \: (2) \\ we \: get \\ a = \frac{25}{b} \\ a = \frac{25}{ \frac{5(5 + \sqrt{21)} }{2} } \\ a = \frac{50}{5(5 + \sqrt{21)} } \\ a = \frac{10}{(5 + \sqrt{21)} }$