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The two consecutive odd positive integers, sum of whose squares is 290 are
- a)13, 15
- b)11, 13
- c)7, 9
- d)5, 7
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The two consecutive odd positive integers, sum of whose squares is 290...
Let first consecutive odd positive integer be x
Secon = x + 2
(x)^2 + ( x + 2 )^2 = 290
x^2 + x^2 + 4 + 4x = 290
2x^2 + 4x = 290 - 4
2x^2 + 4x = 286
2x^2 + 4x - 286 = 0
x^2 + 2x - 143 = 0
x^2 + 13x - 11x - 143 = 0
x ( x + 13 ) - 11 ( x + 13 ) = 0
( x -11) ( x + 13) = 0
x = 11 Or x = -13
Second = 11 + 2 = 13
Hence option (B) is correct .
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Community Answer
The two consecutive odd positive integers, sum of whose squares is 290...
Let first number= (2x+1)second number=(2x+3)According to the question,(2x+1)^2 +(2x+3)^2 =290x^2+2x-35=0x^2+7x-5x-35=0x(x+7)-5(x+7)=0(x+7)(x-5)=0x=-7 {neglected} x=5Since x=5,first number=2×5+1=11second number=2×5+3=13
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The two consecutive odd positive integers, sum of whose squares is 290 area)13, 15b)11, 13c)7, 9d)5, 7Correct answer is option 'B'. Can you explain this answer?
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