Question

दो संख्याओं का ल.स. 495 तथा उनका म.स. 5 है यदि उन सांख्ययो का योग 100 है ।तो उनका अंतर क्या होगा

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Answer 1

Answer:

let the numbers X and Y

X

$x \times y = 495 \times 5 \\ (x + y) {}^{2} = x {}^{2} + y {}^{2} + 2xy \\ put \: the \: values \\ (100) {}^{2} = x {}^{2} + y {}^{2} + 2 \times 495 \times 5 \\ now \: substract \: 4xy \: from \: both \: side\\ 10000 - 4 \times495 \times 5= x {}^{2} + y {}^{2} + 2 \times 495 \times 5 - 4 \times 495 \times 5 \\ 100 = x {}^{2} + y {}^{2} - 2 \times 495 \times 5 \\ (10) {}^{2} = (x - y) {}^{2} \\ x - y = 10$

Answer 2

Answer:

10

Step-by-step explanation:

let numbers be y and (y-100)

1st No. X 2nd No. = lcm X hcf

y(100-y) = 495X55

100y -y² = 2475

-y²+100y-2475 = 0

y²-100y+2475 = 0

y²-55y-45y+2475 = 0

y(y-55) -45(y-55) = 0

(y-45) (y-55) = 0

y = 45      ,        y = 55

first no. = 45

second no. = 100-45 = 55

difference = 55-45 = 10