1. What are the 2 consecutive even natural numbers, sum of whose squares is 52?
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By: anil on 05 May 2019 02.16 am
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 $$x eq -6$$ $$ herefore$$ Numbers are = 4, 6 => Ans - (C)
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eq -6$$ $$ herefore$$ Numbers are = 4, 6 => Ans - (C)