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Question

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


Solution

Let the smaller natural number be x and larger natural number be y

Hence x2=4y → (1)

Given y2x2=45

y24y=45

y24y45=0

y29y+5y45=0

y(y9)+5(y9)=0

(y9)(y+5)=0

(y9)=0 or (y+5)=0

y=9ory=5

But y is natural number, hence y ≠ - 5

Therefore, y = 9

Equation (1) becomes,

x2=4(9)=36

∴ x = 6

Thus the two natural numbers are 6 and 9.


Mathematics
Secondary School Mathematics X
Standard X

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