AP EAMCET · Maths · Sequences and Series
The number of pairs of consecutive positive even integers such that the sum of their squares is 290 is
- A \(0\)
- B \(1\)
- C \(2\)
- D \(3\)
Answer & Solution
Correct Answer
(A) \(0\)
Step-by-step Solution
Detailed explanation
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…
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