Page:Elementary algebra (1896).djvu/202

184 ALGEBRA. EXAMPLES XXI. d.

Find the cube root of each of the following expressions:

1. a^ -h S a"^ -- S a + I. 2. a^x^ - Z a^x'^y- + S axy* - y^. 3. 64 «3 _ 144 «25 + 108 ab^ - 27 b^. 4. 1 + 3 a; + 6 x2 + 7 x3 + 6 x* + 3 ics + a;6. 5. 1 - 6 X + 21 x2 - 44 x3 + 63 X* - 54 x5 + 27 x^. 6. a^--6 a%-Z a^c-{- ab'^-l^ a6c + 3 «c2+8 63_ 12 62^ + 5c2-c3. 7. 8 a6 - 36 a5 + 66 a* - 63 ^3 + 33 ^^2 _ 9 ^^ + ]. 8. 8 x6 + 12 x^ - 30 x* - 35 x^ + 45 a;2 + 27 x - 27. 9. 27 xc - 54 x^a + 117 x^rt^ _ Q xhi^ + 117 xSa* _ 54 xcv' + 27 a^. 10. 27 x6 _ 27 x5 - 18 X* + 17 x3 + 6 x2 - 3 X - 1. 11. 24 x*!/2 + 96 x2?/i - 6 x^^ + x6 - 96 x?/^ + 64 2/6 - 56 x^?/^. 12. 216 + 342 x2 + 171 x* + 27 x^ - 27 x^ - 109 x^ - 108 x.

202. We add some examples of cube root where fractional terms occur in the given expressions.

Ex. Find the cube root of 54 - 27 x^ + - - —. X^ X3

Arrange the expression in ascending powers of x, 8 36 + &4 - 27 x3 Vx2 3 X Vx2J 3x- x(-3x)= - X2 (-3x)2 12 x4 -^+54 X3 -27x3 _18 X + 9x2 1^-18 + 9x2 X4 X x-^ -27x3

EXAMPLES XXI. e.

Find the cube root of each of the following expressions:

1. ±-- 2. 8x3 -^ + ^-L 4^2 3 27x3 27x2 9x ■ 642/3 8y2 -^ y 4 x2?/2 -f 1 Xt - 27 4. ^ - 6 x4 + 12 x2y3 ,,3 8//«.