Question

5. Find two numbers whose sum is 9 times their difference, and the
difference of whose squares is 81.​

Answer 1

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Answer 2

Answer:

Let the no. be x and y

x + y = 9( x - y )

x + y = 9x - 9y

x - 9x + y + 9y = 0

- 8x + 10y = 0

x = 5/4 y (eqn 1)

x^2 - y^2 =81 (eqn 2)

(5/4)^2 - y^2 = 81

25/16 y^2 - y^2 = 81

25 y^2 - 16 ^2 / 16 = 81

9 y^2 = 81 × 16

y^2 = 81× 16/ 9

y^2 = 144

y =√144

y = 12

putting the value of y = 12 in eqn 1

x = 5/4 × 12

x =15

Two numbers are 15 and 12

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