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The two positive numbers differ by 5 and square of their sum is 169 are
- a)2,4
- b)5,6
- c)4,9
- d)3,7
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The two positive numbers differ by 5 and square of their sum is 169 ar...
Explanation:
- Let the two positive numbers be x and y.
- According to the given conditions:
- y = x + 5 (The two positive numbers differ by 5)
- (x + y)2 = 169 (Square of their sum is 169)
- Substituting y = x + 5 in the second condition:
- (x + x + 5)2 = 169
- (2x + 5)2 = 169
- 4x2 + 20x + 25 = 169
- 4x2 + 20x - 144 = 0
- x2 + 5x - 36 = 0
- (x + 9)(x - 4) = 0
- Therefore, the possible values for x are 4 and -9. Since the numbers are positive, x = 4.
- Substituting x = 4 in y = x + 5, we get y = 9.
- Therefore, the two positive numbers are 4 and 9, which is option C.
- Let the two positive numbers be x and y.
- According to the given conditions:
- y = x + 5 (The two positive numbers differ by 5)
- (x + y)2 = 169 (Square of their sum is 169)
- Substituting y = x + 5 in the second condition:
- (x + x + 5)2 = 169
- (2x + 5)2 = 169
- 4x2 + 20x + 25 = 169
- 4x2 + 20x - 144 = 0
- x2 + 5x - 36 = 0
- (x + 9)(x - 4) = 0
- Therefore, the possible values for x are 4 and -9. Since the numbers are positive, x = 4.
- Substituting x = 4 in y = x + 5, we get y = 9.
- Therefore, the two positive numbers are 4 and 9, which is option C.
Most Upvoted Answer
The two positive numbers differ by 5 and square of their sum is 169 ar...
Explanation:
Let the two numbers be x and y, where x is greater than y.
Given, x - y = 5
=> x = y + 5
Also, (x+y)^2 = 169
=> (y+5+y)^2 = 169 (Substituting x = y + 5)
=> (2y+5)^2 = 169
=> 4y^2 + 20y + 25 = 169 (Expanding the square)
=> 4y^2 + 20y - 144 = 0
=> y^2 + 5y - 36 = 0
=> (y + 9)(y - 4) = 0
=> y = -9 or y = 4
Since the numbers are positive, y = 4
Therefore, x = y + 5 = 9
Hence, the two numbers are 4 and 9.
Therefore, option C is the correct answer.
Let the two numbers be x and y, where x is greater than y.
Given, x - y = 5
=> x = y + 5
Also, (x+y)^2 = 169
=> (y+5+y)^2 = 169 (Substituting x = y + 5)
=> (2y+5)^2 = 169
=> 4y^2 + 20y + 25 = 169 (Expanding the square)
=> 4y^2 + 20y - 144 = 0
=> y^2 + 5y - 36 = 0
=> (y + 9)(y - 4) = 0
=> y = -9 or y = 4
Since the numbers are positive, y = 4
Therefore, x = y + 5 = 9
Hence, the two numbers are 4 and 9.
Therefore, option C is the correct answer.
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Community Answer
The two positive numbers differ by 5 and square of their sum is 169 ar...
Let y and 7/3 be the zeros. 3x² - 13x - k = 0 x² - 13/3x - k/3 = 0 sum of the zeros = 13/3 7/3 + y = 13/3 y = 6/3= 2. .............1 product = - k/3 2 * 7/3 = 14/3 k = -14/3*3 answer is -14
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The two positive numbers differ by 5 and square of their sum is 169 area)2,4b)5,6c)4,9d)3,7Correct answer is option 'C'. Can you explain this answer?
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