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Salsk061 [2.6K]
2 years ago
10

Find three consecutive positive integers such that the sum of their squares is 2354. What is the largest integer?

Mathematics
1 answer:
Ilya [14]2 years ago
4 0

Answer:

The largest integer is 29.

Step-by-step explanation:

Let the consecutive positive integers are x, x+1 and x+2.

The square of sum of squares of three consecutive positive integers is 2354 such that,

x^2+(x+1)^2+(x+2)^2=2354\\\\x^2+x^2+2x+1+x^2+4+4x=2354\\\\3x^2+6x+5=2354\\\\3x^2+6x- 2349=0

It is a quadratic equation whose solution is given by :

x = 27 and x = -29

First positive integer = 27

Second positive integer = 27+1 = 28

Third positive integer = 27+2 = 29

Hence, the largest integer is 29.

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We are given a system of inequalities as:

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This  means that the minimal value of the function is 780

and the value exist at (15,30)

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