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Three consecutive natural numbers are such that at the square of middle number exceeds the difference of squares of other two by 60 find the numbers?
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Three consecutive natural numbers are such that at the square of middl...
Problem: Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 60. Find the numbers.
Solution:
Let's assume the three consecutive natural numbers as x, x+1, and x+2.
We are given that the square of the middle number (x+1) exceeds the difference of the squares of the other two (x^2 - (x+2)^2) by 60.
So, we can write the equation as:
(x+1)^2 = x^2 - (x+2)^2 + 60
Expanding the equation:
(x+1)^2 = x^2 - (x^2 + 4x + 4) + 60
x^2 + 2x + 1 = x^2 - x^2 - 4x - 4 + 60
x^2 + 2x + 1 = -4x + 56
x^2 + 6x + 1 - 56 = 0
x^2 + 6x - 55 = 0
Factoring the quadratic equation:
(x + 11)(x - 5) = 0
So, we have two possible values for x:
x + 11 = 0 --> x = -11
or
x - 5 = 0 --> x = 5
Since we need to find three consecutive natural numbers, we disregard the negative value -11.
Therefore, the three consecutive natural numbers are 5, 6, and 7.
Answer: The numbers are 5, 6, and 7.
Solution:
Let's assume the three consecutive natural numbers as x, x+1, and x+2.
We are given that the square of the middle number (x+1) exceeds the difference of the squares of the other two (x^2 - (x+2)^2) by 60.
So, we can write the equation as:
(x+1)^2 = x^2 - (x+2)^2 + 60
Expanding the equation:
(x+1)^2 = x^2 - (x^2 + 4x + 4) + 60
x^2 + 2x + 1 = x^2 - x^2 - 4x - 4 + 60
x^2 + 2x + 1 = -4x + 56
x^2 + 6x + 1 - 56 = 0
x^2 + 6x - 55 = 0
Factoring the quadratic equation:
(x + 11)(x - 5) = 0
So, we have two possible values for x:
x + 11 = 0 --> x = -11
or
x - 5 = 0 --> x = 5
Since we need to find three consecutive natural numbers, we disregard the negative value -11.
Therefore, the three consecutive natural numbers are 5, 6, and 7.
Answer: The numbers are 5, 6, and 7.
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Three consecutive natural numbers are such that at the square of middle number exceeds the difference of squares of other two by 60 find the numbers? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Three consecutive natural numbers are such that at the square of middle number exceeds the difference of squares of other two by 60 find the numbers? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three consecutive natural numbers are such that at the square of middle number exceeds the difference of squares of other two by 60 find the numbers?.
Three consecutive natural numbers are such that at the square of middle number exceeds the difference of squares of other two by 60 find the numbers? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Three consecutive natural numbers are such that at the square of middle number exceeds the difference of squares of other two by 60 find the numbers? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three consecutive natural numbers are such that at the square of middle number exceeds the difference of squares of other two by 60 find the numbers?.
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