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AP EAMCET20228 Jul 2022Evening ShiftMathematicsSequences and SeriesActual

The number of pairs of consecutive positive even integers such that the sum of their squares is 290 is

Options

  1. A0
  2. B1
  3. C2
  4. D3

Correct answer

A. 0

Step-by-step solution

Let x and x+2 be two consecutive positive even integers. Given, x^2+(x+2)^2=290 x^2+x^2+4 x+4-290=0 array ll & 2 x^2+4 x-286=0 & x^2+2 x-143=0 array x=-13,11 [ -13 not postive integer and x=13 , is not even positive integer] Hence, number of solutions =0

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