Mathematics
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
Quadratic Equations
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Answer
Let two integers be x and x - 2.
Give,
Sum of squares = 52
⇒ x2 + (x - 2)2 = 52
⇒ x2 + x2 + 4 - 4x = 52
⇒ 2x2 - 4x + 4 - 52 = 0
⇒ 2x2 - 4x - 48 = 0
⇒ 2(x2 - 2x - 24) = 0
⇒ x2 - 2x - 24 = 0
⇒ x2 - 6x + 4x - 24 = 0
⇒ x(x - 6) + 4(x - 6) = 0
⇒ (x + 4)(x - 6) = 0
⇒ x + 4 = 0 or x - 6 = 0
⇒ x = -4 or x = 6.
If x = -4,
x - 2 = -4 - 2 = -6.
If x = 6,
x - 2 = 6 - 2 = 4.
Numbers = -4 and -6 or 6 and 4.
Hence, Option 4 is the correct option.
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