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The difference of two positive integers is 3 and the sum of their squares is 89. Taking the smaller integer as x form a quadratic equation and solve it to find the integers. The integers are.
- a)(7, 4)
- b)(5, 8)
- c)(3, 6)
- d)(2, 5)
Correct answer is option 'B'. Can you explain this answer?
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The difference of two positive integers is 3 and the sum of their squa...
Given data
- Difference of two positive integers = 3
- Sum of their squares = 89
- Smaller integer = x
Forming the equation
- Let the larger integer be y
- As the difference of two positive integers is 3, we have y = x + 3
- The sum of their squares is 89, so x^2 + y^2 = 89
- Substituting y = x + 3, we get x^2 + (x+3)^2 = 89
- Simplifying the equation, we get x^2 + x^2 + 6x + 9 = 89
- Combining like terms, we get 2x^2 + 6x - 80 = 0
- Dividing both sides by 2, we get x^2 + 3x - 40 = 0
Solving the equation
- To solve the quadratic equation x^2 + 3x - 40 = 0, we can use factorization or the quadratic formula.
- Factoring the equation, we get (x+8)(x-5) = 0
- Therefore, the solutions are x = -8 and x = 5, but as the smaller integer cannot be negative, we take x = 5.
- Substituting x = 5 in y = x + 3, we get y = 8
Final answer
- The two positive integers are 5 and 8.
- Therefore, option B is the correct answer.
- Difference of two positive integers = 3
- Sum of their squares = 89
- Smaller integer = x
Forming the equation
- Let the larger integer be y
- As the difference of two positive integers is 3, we have y = x + 3
- The sum of their squares is 89, so x^2 + y^2 = 89
- Substituting y = x + 3, we get x^2 + (x+3)^2 = 89
- Simplifying the equation, we get x^2 + x^2 + 6x + 9 = 89
- Combining like terms, we get 2x^2 + 6x - 80 = 0
- Dividing both sides by 2, we get x^2 + 3x - 40 = 0
Solving the equation
- To solve the quadratic equation x^2 + 3x - 40 = 0, we can use factorization or the quadratic formula.
- Factoring the equation, we get (x+8)(x-5) = 0
- Therefore, the solutions are x = -8 and x = 5, but as the smaller integer cannot be negative, we take x = 5.
- Substituting x = 5 in y = x + 3, we get y = 8
Final answer
- The two positive integers are 5 and 8.
- Therefore, option B is the correct answer.
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The difference of two positive integers is 3 and the sum of their squares is 89. Taking the smaller integer as x form a quadratic equation and solve it to find the integers. The integers are.a)(7, 4)b)(5, 8)c)(3, 6)d)(2, 5)Correct answer is option 'B'. Can you explain this answer?
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