Question 85

What are the 2 consecutive even natural numbers, sum of whose squares is 52?

Solution

Let the consecutive even natural numbers be $$x$$ , $$(x+2)$$

Sum of their squares = $$(x)^2+(x+2)^2=52$$

=> $$x^2+(x^2+4x+4)=52$$

=> $$2x^2+4x+4-52=0$$

=> $$x^2+2x-24=0$$

=> $$x^2+6x-4x-24=0$$

=> $$x(x+6)-4(x+6)=0$$

=> $$(x-4)(x+6)=0$$

=> $$x=4,-6$$

Since, the numbers are natural, thus $$x \neq -6$$

$$\therefore$$ Numbers are = 4, 6

=> Ans - (C)

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