The sum of the squares of two consecutive integers is 41. The integers are : 1. 4 and -5 or -4 and 5 2. 4 and 5 or -4 and -5 3. 3 and 4 or -4 and -3 4. 6 and 3 or -6 and -3

Let two consecutive integers be x and x + 1. Given, Sum of squares of two consecutive integers = 41. ⇒ x 2 + (x + 1) 2 = 41 ⇒ x 2 + x 2 + 1 + 2x = 41 ⇒ 2x 2 + 2x = 41 - 1 ⇒ 2x 2 + 2x = 40 ⇒ 2(x 2 + x) = 40 ⇒ x 2 + x = ⇒ x 2 + x = 20 ⇒ x 2 + x - 20 = 0 ⇒ x 2 + 5x - 4x - 20 = 0 ⇒ x(x + 5) - 4(x + 5) = 0 ⇒ (x - 4)(x + 5) = 0 ⇒ x - 4 = 0 or x + 5 = 0 ⇒ x = 4 or x = -5 If x = 4, ⇒ x + 1 = 4 + 1 = 5. If x = -5, ⇒ x + 1 = -5 + 1 = -4. Numbers = 4 and 5 or -4 and -5. Hence, Option 2 is the correct option.

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The product of two consecutive even whole numbers is 24, the numbers are :
-8 and -3
3 and 8
-4 and -6
4 and 6

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Two integers differ by 2 and sum of their squares is 52. The integers are :
4 and 6
4 or 6
-4 or 6
-4 and -6 or 6 and 4

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Mathematics

The sum of the squares of two consecutive integers is 41. The integers are :
4 and -5 or -4 and 5
4 and 5 or -4 and -5
3 and 4 or -4 and -3
6 and 3 or -6 and -3

Quadratic Equations

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The product of two consecutive even whole numbers is 24, the numbers are :
-8 and -3
3 and 8
-4 and -6
4 and 6

Two integers differ by 2 and sum of their squares is 52. The integers are :
4 and 6
4 or 6
-4 or 6
-4 and -6 or 6 and 4

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The sum of the squares of two consecutive integers is 41. The integers are :4 and -5 or -4 and 54 and 5 or -4 and -53 and 4 or -4 and -36 and 3 or -6 and -3

Quadratic Equations

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The product of two consecutive even whole numbers is 24, the numbers are :-8 and -33 and 8-4 and -64 and 6

Two integers differ by 2 and sum of their squares is 52. The integers are :4 and 64 or 6-4 or 6-4 and -6 or 6 and 4

The sum of the squares of two consecutive integers is 41. The integers are :
4 and -5 or -4 and 5
4 and 5 or -4 and -5
3 and 4 or -4 and -3
6 and 3 or -6 and -3

The product of two consecutive even whole numbers is 24, the numbers are :
-8 and -3
3 and 8
-4 and -6
4 and 6

Two integers differ by 2 and sum of their squares is 52. The integers are :
4 and 6
4 or 6
-4 or 6
-4 and -6 or 6 and 4