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Find two consecutive positive integers, sum of whose squares is 365.

Q4.    Find two consecutive positive integers, the sum of whose squares is 365.

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Let the two consecutive integers be 'x'\ and\ 'x+1'.

Then the sum of squares is 365.

.x^2+ (x+1)^2 = 365

\Rightarrow x^2+x^2+1+2x = 365

\Rightarrow x^2+x-182 = 0

\Rightarrow x^2 - 13x+14x+182 = 0

\Rightarrow x(x-13)+14(x-13) = 0

\Rightarrow (x-13)(x-14) = 0

\Rightarrow x =13\ or\ 14

Hence, the two consecutive integers are 13\ and\ 14.

 

 

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