RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 10. Quadratic Equations

Subject: Maths - Class 10th

Q. No. 21 of Exercise 10E

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21

Find two natural numbers, the sum of whose squares is 25 times their sum and also equal to 50 times their difference.

Let the two natural numbers be x and y.

According to the question


x2 + y2 = 25(x + y) – – – – – (1)


x2 + y2 = 50(x – y) – – – – (2)


From (1) and (2) we get


25(x + y) = 50(x – y)


x + y = 2(x – y)


x + y = 2x – 2y


y + 2y = 2x – x


3y = x – – – – – (3)


From (2) and (3) we get


(3y)2 + y2 = 50(3y – y)


9y2 + y2 = 50(3y – y)


10 y2 = 100y


y = 10


From (3) we have,


x = 3y = 3.10 = 30


Hence the two natural numbers are 30 and 10.


Chapter Exercises

Exercise 10A
Exercise 10B
Exercise 10C
Exercise 10D
Exercise 10E
Exercise 10F

More Exercise Questions

1

The sum of a natural number and its square is 156. Find the number.
2

The sum of a natural number and its positive square root is 132. Find the number.
3

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4

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5

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6

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7

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8

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9

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10

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11

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12

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13

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14

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15

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16

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17

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18

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19

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20

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21

Find two natural numbers, the sum of whose squares is 25 times their sum and also equal to 50 times their difference.
22

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23

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24

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25

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26

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27

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28

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29

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30

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31

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32

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33

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34

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35

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36

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37

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38

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40

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41

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42

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43

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44

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45

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46

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47

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48

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49

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50

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51

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52

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53

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54

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55

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56

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57

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58

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59

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60

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61

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