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Two consecutive even positive integers, sum of the squares of which is 1060 are
- a)12 and 14
- b)22 and 24
- c)20 and 22
- d)16 and 18
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Two consecutive even positive integers, sum of the squares of which is...
**Solution:**
Let's assume the two consecutive even positive integers as x and x+2.
According to the given information, the sum of the squares of these two integers is 1060.
So, we can form the equation as follows:
x^2 + (x+2)^2 = 1060
Expanding the equation:
x^2 + x^2 + 4x + 4 = 1060
Combining like terms:
2x^2 + 4x + 4 = 1060
Subtracting 1060 from both sides:
2x^2 + 4x - 1056 = 0
Dividing the equation by 2 to simplify:
x^2 + 2x - 528 = 0
**Factoring the quadratic equation:**
To find the factors of -528 that add up to 2, we can use trial and error or apply the quadratic formula. We can see that the factors are 22 and -24.
So, the two consecutive even positive integers are 22 and 24.
The correct answer is option **B) 22 and 24**.
Let's assume the two consecutive even positive integers as x and x+2.
According to the given information, the sum of the squares of these two integers is 1060.
So, we can form the equation as follows:
x^2 + (x+2)^2 = 1060
Expanding the equation:
x^2 + x^2 + 4x + 4 = 1060
Combining like terms:
2x^2 + 4x + 4 = 1060
Subtracting 1060 from both sides:
2x^2 + 4x - 1056 = 0
Dividing the equation by 2 to simplify:
x^2 + 2x - 528 = 0
**Factoring the quadratic equation:**
To find the factors of -528 that add up to 2, we can use trial and error or apply the quadratic formula. We can see that the factors are 22 and -24.
So, the two consecutive even positive integers are 22 and 24.
The correct answer is option **B) 22 and 24**.
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Community Answer
Two consecutive even positive integers, sum of the squares of which is...
The best way for it is trial and error
(22)²+(24)²= 484+576= 1060
(22)²+(24)²= 484+576= 1060
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Two consecutive even positive integers, sum of the squares of which is 1060 area)12 and 14b)22 and 24c)20 and 22d)16 and 18Correct answer is option 'B'. Can you explain this answer?
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