Question

The difference of square of two natural numbers is 45. The square of the smaller number is four times the larger number. Find the two numbers.

Answer 1

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Answer:

the two numbers are 9 and 6

Step-by-step explanation:

x^2 - y^2 = 45

y^2 = 4x

x^2 - 4x - 45 = 0

(x - 9)(x + 5)=0

x = 9......(1)

y^2 = 4×9

y^2 = 36

y = 6

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Answer 2

Let the two no. be x and y such that y <x.

From the given conditions, we have

x^2 - y^2 =45.....(1)

y^2 = 45......(2)

Using (2) in (1)

x^2 - 4x - 45=0

(x-9) ( x+5)

x=9 (Rejecting the negative value of x)

From (2) we get, y= 6 or -6

Rejecting the negative value of , we have y= 6

Thus the two no. are 9 and 6.