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,
[tex]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[/tex]
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.
