Question-87556

Question Number 87556 by M±th+et£s last updated on 05/Apr/20

Commented by jagoll last updated on 05/Apr/20

x^{3} - {2 x}^{2} + 7 x - 1 = a {(x - 2)}^{2} +

b (x - 3) {(x - 2)}^{2} + c {(x - 3)}^{2} {(x - 2)}^{2} +

d {(x - 3)}^{3} + e {(x - 3)}^{3} (x - 2)

Answered by $@ty@m123 last updated on 05/Apr/20

L e t \frac{x^{3} - 2 x^{2} + 7 x - 1}{{(x - 3)}^{3} {(x - 2)}^{2}} = \frac{A}{{(x - 3)}^{3}} + \frac{B}{{(x - 3)}^{2}}

+ \frac{C}{(x - 3)} + \frac{D}{{(x - 2)}^{2}} + \frac{E}{x - 2}

\Rightarrow A {(x - 2)}^{2} + B (x - 3) {(x - 2)}^{2} + C {(x - 3)}^{2} {(x - 2)}^{2}

+ D {(x - 3)}^{2} + E {(x - 3)}^{3} (x - 2) =

x^{3} - 2 x^{2} + 7 x - 1 \dots . (i)

P u t x = 0 i n (i)

\Rightarrow 4 A + 12 B + 36 C + 9 D + 54 E = - 1 \dots (i i)

P u t x = 1 i n (i)

A - 2 B + 4 C + 4 D - 8 E = 5 \dots . (i i i)

P u t x = 2 i n (i)

D = 8 - 8 + 14 - 1 = 13

P u t x = 3 i n (i)

A = 27 - 18 + 20 = 29

N o w d o i t y o u r s e l f :

P u t v a l u e s o f A & D i n (i i) & (i i i)

a n d f o r m e q u a t i o n (i v) & (v)

P u t x = 4 i n (i) a n d f o r m e q u a t i o n (v i)

S o l v e (i v), (v) & (v i) f o r B, C & E u s i n g

{C r a m e r}^{'} s R u l e .

Commented by peter frank last updated on 05/Apr/20

t h a n k y o u

Commented by M±th+et£s last updated on 05/Apr/20

g o d b l e s s y o u s i r