1. Find 2 consecutive natural numbers, sum of whose squares is 25.
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By: anil on 05 May 2019 02.16 am
Let the consecutive natural numbers be $$x$$ , $$(x+1)$$ Sum of their squares = $$(x)^2+(x+1)^2=25$$ => $$x^2+(x^2+2x+1)=25$$ => $$2x^2+2x+1-25=0$$ => $$x^2+x-12=0$$ => $$x^2+4x-3x-12=0$$ => $$x(x+4)-3(x+4)=0$$ => $$(x+4)(x-3)=0$$ => $$x=-4,3$$ Since, the numbers are natural, thus $$x eq -4$$ $$ herefore$$ Numbers are = 3, 4 => Ans - (B)
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eq -4$$ $$ herefore$$ Numbers are = 3, 4 => Ans - (B)