Given-f-x-ax-5-bx-4-cx-3-dx-2-ex-f-f-1-1-f-2-1-4-f-3-1-9-f-4-1-16-f-5-1-25-and-f-6-1-36-Value-of-f-8-

Question Number 167925 by naka3546 last updated on 29/Mar/22

Given f (x) = {a x}^{5} + {b x}^{4} + {c x}^{3} + {d x}^{2} + e x + f .

f (1) = 1, f (2) = \frac{1}{4}, f (3) = \frac{1}{9}, f (4) = \frac{1}{16},

f (5) = \frac{1}{25}, a n d f (6) = \frac{1}{36} .

V a l u e o f f (8) = ?

Answered by mr W last updated on 29/Mar/22

f (8) = [\begin{matrix} 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 32 & 16 & 8 & 4 & 2 & 1 & 1 / 4 \\ 243 & 81 & 27 & 9 & 3 & 1 & 1 / 9 \\ 1024 & 256 & 64 & 16 & 4 & 1 & 1 / 16 \\ 3125 & 625 & 125 & 25 & 5 & 1 & 1 / 25 \\ 7776 & 1296 & 216 & 36 & 6 & 1 & 1 / 36 \\ 32768 & 4096 & 512 & 64 & 8 & 1 & 0 \end{matrix}] / [\begin{matrix} 1 & 1 & 1 & 1 & 1 & 1 & 0 \\ 32 & 16 & 8 & 4 & 2 & 1 & 0 \\ 243 & 81 & 27 & 9 & 3 & 1 & 0 \\ 1024 & 256 & 64 & 16 & 4 & 1 & 0 \\ 3125 & 625 & 125 & 25 & 5 & 1 & 0 \\ 7776 & 1296 & 216 & 36 & 6 & 1 & 0 \\ 32768 & 4096 & 512 & 64 & 8 & 1 & - 1 \end{matrix}]

= - \frac{77328}{34560}

= - \frac{179}{80}

Commented by naka3546 last updated on 29/Mar/22

Thank you, sir .

Commented by Tawa11 last updated on 30/Mar/22

Great sir .

What is the rule to set the matrix sir . God bless you .

Commented by mr W last updated on 30/Mar/22

s o l v i n g s y s t e m o f 7 l i n e a r e q u a t i o n s

w i t h {C r a m e r}^{'} s r u l e .

s e e a l s o Q 167839

Commented by mr W last updated on 30/Mar/22

f (1) = a + b + c + d + e + f = 1

f (2) = 2^{5} a + 2^{4} b + 2^{3} c + 2^{2} d + 2 e + f = 1 / 4

f (3) = 3^{5} a + 3^{4} b + 3^{3} c + 3^{2} d + 3 e + f = 1 / 9

\dots .

f (6) = 6^{5} a + 6^{4} b + 6^{3} c + 6^{2} d + 6 e + f = 1 / 36

f (8) = 8^{5} a + 8^{4} b + 8^{3} c + 8^{2} d + 8 e + f = s s a y

w e g e t 7 e q u a t i o n s :

a + b + c + d + e + f + 0 s = 1

2^{5} a + 2^{4} b + 2^{3} c + 2^{2} d + 2 e + f + 0 s = 1 / 4

3^{5} a + 3^{4} b + 3^{3} c + 3^{2} d + 3 e + f + 0 s = 1 / 9

\dots

6^{5} a + 6^{4} b + 6^{3} c + 6^{2} d + 6 e + f + 0 s = 1 / 36

8^{5} a + 8^{4} b + 8^{3} c + 8^{2} d + 8 e + f - s = 0

n o w w e c a n s o l v e a, b, c, d, e, f, s .

Commented by Tawa11 last updated on 30/Mar/22

Thanks sir . I appreciate .

Facebook Tweet Pin