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lara31 [8.8K]
2 years ago
15

The sum of the squares of two consecutive even integers is 884. find the integers

Mathematics
1 answer:
andriy [413]2 years ago
3 0
2x + 2x +2 are the integers
4x^2 + 4x^2 +8x +4 =884 (The sum of the integers squared)
8 x^2 +8x -880 = 0

x = 10
Therefore, the integers are:
20 and 22




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we have

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Divide both sides by -2

2.75=(x^{2} -5x+2.5^{2})

Rewrite as perfect squares

2.75=(x-2.5)^{2}

Taking the square roots of both sides (square root property of equality)

x-2.5=(+/-)\sqrt{2.75}

Remember that

\sqrt{2.75}=\sqrt{\frac{11}{4}}= \frac{\sqrt{11}}{2}

x-2.5=(+/-)\frac{\sqrt{11}}{2}

x=2.5(+/-)\frac{\sqrt{11}}{2}

x=2.5+\frac{\sqrt{11}}{2}=\frac{5+\sqrt{11}}{2}

x=2.5-\frac{\sqrt{11}}{2}=\frac{5-\sqrt{11}}{2}

<u>the answer is</u>

The solutions are

x=\frac{5+\sqrt{11}}{2}

x=\frac{5-\sqrt{11}}{2}


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