S737 2 -S736 *S738 =(a737 +b737 +c737 )2 -(a736 +b736 +c736 )(a738 +b738 +c738 )=
a1474 +a737 b737 +a737 c737 +b737 a737 +b1474 +b737 c737 +c737 a737 +c737 b737 +c1474 -
-(a1474 +a736 b738 +a736 c738 +b736 a738 +b1474 +b736 c738 +c736 a738 +c736 b738 +c1474 )=
2a737 b737 +2a737 c737 +2b737 c737 -a736 (b738 +c738 )-b736 (a738 +c738 )-c736 (a738 +b738 )
It is known that:
4.5=a+b+c
22.25=a2 +b2 +c2
104.625=a3 +b3 +c3
Since the system is symmetric we can consider only one solution:
c=4.5-a-b
22.25=a2 +b2 +(4.5-a-b)2
b=1 4 ( − − 12 ∗ a 2 + 36 ∗ a + 97 − 2 a + 9 ) \frac{1}{4}(-\sqrt{-12*a^2+36*a+97}-2a+9) 4 1 ( − − 12 ∗ a 2 + 36 ∗ a + 97 − 2 a + 9 )
104.625=a3 +( 1 4 ( − − 12 ∗ a 2 + 36 ∗ a + 97 − 2 a + 9 ) ) 3 (\frac{1}{4}(-\sqrt{-12*a^2+36*a+97}-2a+9))^3 ( 4 1 ( − − 12 ∗ a 2 + 36 ∗ a + 97 − 2 a + 9 ) ) 3 +( 4.5 − a − 1 4 ( − − 12 ∗ a 2 + 36 ∗ a + 97 − 2 a + 9 ) ) 3 (4.5-a-\frac{1}{4}(-\sqrt{-12*a^2+36*a+97}-2a+9))^3 ( 4.5 − a − 4 1 ( − − 12 ∗ a 2 + 36 ∗ a + 97 − 2 a + 9 ) ) 3
a=0
b=9 4 − 97 4 \frac{9}{4}-\frac{\sqrt{97}}{4} 4 9 − 4 97
c=9 4 + 97 4 \frac{9}{4}+\frac{\sqrt{97}}{4} 4 9 + 4 97
S737 2 -S736 *S738 =2b737 c737 -b736 (c738 )-c736 (b738 )=2( 9 4 − 97 4 ) 737 (\frac{9}{4}-\frac{\sqrt{97}}{4})^{737} ( 4 9 − 4 97 ) 737 * ( 9 4 + 97 4 ) 737 (\frac{9}{4}+\frac{\sqrt{97}}{4})^{737} ( 4 9 + 4 97 ) 737 -( 9 4 − 97 4 ) 736 (\frac{9}{4}-\frac{\sqrt{97}}{4})^{736} ( 4 9 − 4 97 ) 736 ( 9 4 + 97 4 ) 738 (\frac{9}{4}+\frac{\sqrt{97}}{4})^{738} ( 4 9 + 4 97 ) 738 -( 9 4 − 97 4 ) 738 (\frac{9}{4}-\frac{\sqrt{97}}{4})^{738} ( 4 9 − 4 97 ) 738 ( 9 4 + 97 4 ) 736 (\frac{9}{4}+\frac{\sqrt{97}}{4})^{736} ( 4 9 + 4 97 ) 736 =-2-( 9 4 + 97 4 ) 2 (\frac{9}{4}+\frac{\sqrt{97}}{4})^{2} ( 4 9 + 4 97 ) 2 -( 9 4 − 97 4 ) 2 (\frac{9}{4}-\frac{\sqrt{97}}{4})^{2} ( 4 9 − 4 97 ) 2 =
-2-1 8 ( 89 + 9 97 ) \frac{1}{8}(89+9\sqrt{97}) 8 1 ( 89 + 9 97 ) -1 8 ( 89 − 9 97 ) \frac{1}{8}(89-9\sqrt{97}) 8 1 ( 89 − 9 97 ) =-2-89/8-89/8=2-89/4=-81 4 \frac{81}{4} 4 81
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