Quadratic Equations
CBSE 2026 Board Exam Set 1 (Code 30/1/1)
CBSE_BOARD_PYQ_2026_30_1_1
Grade 10
Question:
[Section C]
Find two consecutive odd positive integers, sum of whose squares is $290$.
Step-by-Step Solution
Key Concept: Let integers be $x, x+2$. $x^2 + (x+2)^2 = 290 \Rightarrow 2x^2 + 4x - 286 = 0 \Rightarrow x^2 + 2x - 143 = 0$.
$x^2 + (x + 2)^2 = 290 \Rightarrow x^2 + 2x - 143 = 0 \Rightarrow (x + 13)(x - 11) = 0$. [1.5 Marks]
Since $x > 0$, $x = 11$. Integers are $11$ and $13$. [1.5 Marks]
Correct Answer: Integers are $11$ and $13$
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