Q51 / 160 · AP EAMCET 2022 (08 Jul Shift 2) · Mathematics

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

  • Correct answer
    A
    $0$
  • B
    $1$
  • C
    $2$
  • D
    $3$

Solution

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

Hence, the correct answer is option: 'A'.

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