56 BOOK OF MATHEMATICAL PROBLEMS. 



257. The equation L -r-+ V+ ...H =- = will iv- 



x + 6 X x + b a x + b 



duce to a simple equation if 



1 + a,+... + a ll 0, 



a l b l + aj> a + ... + 0^ = 0, 

 =0, 



A- 3 +A"-' + ".+A"- 8 = , 



and the value of x will in that case be 



258. Prove that 



(a + b + c + d)* - 4 (a + 6 + c + d) (be + ca + ah + ad + bd+ cd) 



+ 8 (bed + cda + dab + abc) 

 = (b + c - a - d) (c + a - 6 - d) (a + b - c - d). 



259. Having given 



' + c' = Q, a 3 + b 3 + c 3 + a* + b' 3 + c a = 



. 

 provet hat 



260. If a, 6, c be three positive quantities, of which any two 

 are together greater than the third, 



unless a, 6, c are all equal. 

 261. Prove that 



