Observe that the sum of the same powers of two numbers is divisible by the sum of the numbers only when the powers are odd. PRINCIPLES. — 1. ж" — у" гя always divisible by x — y. 2. xn — у" is divisible by x + y only when n is even. 3. x"... The Elements of Algebra - Página 77por George W. Lilley - 1892 - 402 páginasVista completa - Acerca de este libro
| 1860 - 294 páginas
...EVANS, Madison University, Hamilton, NY x a by xc dy m Find x by quadratics. Since the sum of the fifth powers of two numbers is divisible by the sum of the numbers, both numerator and denominator of the first member of the given equation is divisible by 2a: + af-... | |
| George Albert Wentworth - 1881 - 406 páginas
...(32 a5 - 243 65) H- (2 a - 3 6). CASE II. From these results it may be assumed that : 103. The sum of two equal odd powers of two numbers is divisible by the sum of the numbers. EXERCISE XXV. Write by inspection the results in the following examples : 1. (a;s + ys)-=-(a; + y).... | |
| George Albert Wentworth - 1886 - 284 páginas
...— ax -f- a2, and \y = ж4 - ar'y + *y _ жу» + у4, x-тУ and so on, it follows that the sum of two equal odd powers of two numbers is divisible by the sum of the numbers. Ex. 4O. Resolve into factors : 1. a^ + y2. 6. 216a2 + 512c2. 2. arЧ-8. 7. 3. ^ + 216. 8. 4. ys + 64z2.... | |
| George Albert Wentworth - 1888 - 518 páginas
...r'y + 36 ^y2 - 24 .ту3 + 16y4. ' From these results it may be assumed that : 103. The sum of ¿wo equal odd powers of two numbers is divisible by the sum of the numbers. EXERCISE XXV. Write by inspection the results in the following examples : 1. (,f + f)-i.(x + y). 5.... | |
| George Albert Wentworth - 1888 - 350 páginas
...81a;4- 54^y + 36^y2- 24V+ 16y4. From these results it may be assumed that : 103. 7%e swra q/" <wo eywaZ odd powers of two numbers is divisible by the sum of the numbers. EXERCISE XXV. Write by inspection the results in the following examples ; 1. (a* + y3)-i-(x + y). 5.... | |
| George Albert Wentworth - 1888 - 514 páginas
...<¿±&. = a< _ aз¿ + a2¿2 — a¿8 + ¿4 a + о In general, it will be found that the sum of two like odd powers of two numbers is divisible by the sum of the numbers. Compare the quotients in (3) and (4) with those in (1) and (2). (5) -= = (6) ^~f = . > У IJ In general,... | |
| Edward Albert Bowser - 1888 - 868 páginas
...the sum of the numbers. x™ + y" is divisible by x + y if n be any odd whole number. (3) That is : the sum of any two equal odd powers of two numbers is always divisible by the sum of the numbers. x™ + »/" is never divisible by x + y or x — y, when... | |
| George P. Lilley - 1894 - 522 páginas
...and so on. a + 6 a + 6 Hence, in general, it will be found that, The difference of any two equal even powers of two numbers is divisible by the sum of the numbers. VI. The signs are alternately + and —. Hence, the principle may be applied to different classes of... | |
| William James Milne - 1901 - 462 páginas
...— y. x + y x + y уг, Eem., — , Eem., From the above we infer that the difference of the same powers of two numbers is divisible by the sum of the numbers only when tlje powers are even. 3. x — y x — y x — y = ж2 + xy + y2, Eem., 2 y3. = x3 + x'y... | |
| William James Milne - 1902 - 620 páginas
...— з?у + yhf — xf + y4, Rem., — 2?A From the above we infer that the difference of the same powers of two numbers is divisible by the sum of the numbers only when the powers are even. 3. zr;r = a; + y, Rem., 2y*. у + ?/2, Rem., xy xt + yt xy ^,¿4 = *"... | |
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