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The Sum of the Squares of Two Consecutive Even Numbers is 340. Find the Numbers. - CBSE Class 10 - Mathematics

ConceptSolutions of Quadratic Equations by Completing the Square

Question

The sum of the squares of two consecutive even numbers is 340. Find the numbers.

Solution

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

Then according to question,

$x^2 + \left( x + 2 \right)^2 = 340$

$\Rightarrow x^2 + x^2 + 4x + 4 = 340$

$\Rightarrow 2 x^2 + 4x - 336 = 0$

$\Rightarrow x^2 + 2x - 168 = 0$

$\Rightarrow x^2 + 14x - 12x - 168 = 0$

$\Rightarrow x(x + 14) - 12(x + 14) = 0$

$\Rightarrow (x - 12)(x + 14) = 0$

$\Rightarrow x - 12 = 0 \text { or } x + 14 = 0$

$\Rightarrow x = 12 \text { or } x = - 14$

Since, being an even number,

Therefore, x = 12.

Then another number will be $x + 2 = 12 + 2 = 14$

Thus, the two consecutive even numbers are 12 and 14.

Is there an error in this question or solution?

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Solution The Sum of the Squares of Two Consecutive Even Numbers is 340. Find the Numbers. Concept: Solutions of Quadratic Equations by Completing the Square.
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