Suma kwadratów trzech kolejnych liczb nieparzystych wynosi 155. Wyznacz te liczby.
(2n+1)²+(2n+3)²+(2n+5)²=155
4n²+4n+1+4n²+12n+9+4n²+20n+25=155
12n²+36n-120=0
n²+3n-10=0
n²-2n+5n-10=0
n(n-2)+5(n-2)=0
(n+5)(n-2)=0
n=-5 ∨ n=2
2*(-5)+1=-9
2*(-5)+3=-7
2*(-5)+5=-5
lub
2*2+1=5
2*2+3=7
2*2+5=9
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(2n+1)²+(2n+3)²+(2n+5)²=155
4n²+4n+1+4n²+12n+9+4n²+20n+25=155
12n²+36n-120=0
n²+3n-10=0
n²-2n+5n-10=0
n(n-2)+5(n-2)=0
(n+5)(n-2)=0
n=-5 ∨ n=2
2*(-5)+1=-9
2*(-5)+3=-7
2*(-5)+5=-5
lub
2*2+1=5
2*2+3=7
2*2+5=9