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Find Two Consecutive Odd Positive Integers, Sum of Whose Squares is 970. - CBSE Class 10 - Mathematics

ConceptSolutions of Quadratic Equations by Completing the Square

Question

Find two consecutive odd positive integers, sum of whose squares is 970.

Solution

Let one of the number be x then other number is x + 2.

Then according to question,

$x^2 + \left( x + 2 \right)^2 = 970$

$\Rightarrow x^2 + x^2 + 4x + 4 = 970$

$\Rightarrow 2 x^2 + 4x - 966 = 0$

$\Rightarrow x^2 + 2x - 483 = 0$

$\Rightarrow x^2 + 23x - 21x - 483 = 0$

$\Rightarrow x(x + 23) - 21(x + 23) = 0$

$\Rightarrow (x - 21)(x + 23) = 0$

$\Rightarrow x - 21 = 0 \text { or } x + 23 = 0$

$\Rightarrow x = 21 \text { or } x = - 23$

Since, being an odd positive integer,

Therefore, x = 21.

Then another number will be $x + 2 = 21 + 2 = 23$

Thus, the two consecutive odd positive integers are 21 and 23.

Is there an error in this question or solution?

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Solution Find Two Consecutive Odd Positive Integers, Sum of Whose Squares is 970. Concept: Solutions of Quadratic Equations by Completing the Square.
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