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Quadratic Equations — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsQuadratic Equations3 Marks
Question
Find the consecutive even integers whose squares have the sum $340.$
✓

Answer

Let the consecutive even integers be $2x$ and $2x + 2$
Then according to the given hypothesis,
$(2x)^2 + (2x + 2)^2 = 340$
$4x^2 + 4x^2 + 8x + 4 - 340 = 0$
$\Rightarrow 8x^2 + 8x - 336 = 0$
$\Rightarrow x^2 + x - 42 = 0$
$\Rightarrow x^2 + 7x - 6x - 42 = 0$
$\Rightarrow x(x + 7) - 6(x + 7) = 0$
$\Rightarrow (x + 7)(x - 6) = 0$
$\Rightarrow x = -7$ or $x = 6$
Considering, the positive integers of $x = 6$
$\Rightarrow 2x = 12$ and $2x + 2 = 14$
$\therefore$ The two consecutive even integers are $12$ and $14$

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