Question 56

What is the value of 2 consecutive natural numbers, sum of whose squares is 145?

Solution

Let the consecutive natural numbers be $$(x)$$ and $$(x + 1)$$

Sum of squares = $$(x)^2 + (x + 1)^2 = 145$$

=> $$x^2 + x^2 + 2x + 1 = 145$$

=> $$2x^2 + 2x - 144 = 0$$

=> $$x^2 + x - 72 = 0$$

=> $$x^2 + 9x - 8x - 72 = 0$$

=> $$x(x + 9) - 8(x + 9) = 0$$

=> $$(x - 8) (x + 9) = 0$$

=> $$x = 8 , -9$$

Since, $$x$$ is a natural number, it can't be negative.

$$\therefore$$ The natural numbers are 8 and 9

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