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Jonask
 one year ago
Best ResponseYou've already chosen the best response.1\[\color{brown}{f(x)+(x+1)^3=2f(x+1)}\]

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.0Find \(\color{#C00}{f(10)}\)

Jonask
 one year ago
Best ResponseYou've already chosen the best response.1lol thanks for posting the full question @ParthKohli

Jonask
 one year ago
Best ResponseYou've already chosen the best response.1wat to do next i 3 variables 2 equations??

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.0\[f(0) = 2f(1)  1 \\ f(1) = 2f(2)  8\]So\[f(0) = 2(2f(2)  8) = 4f(2)  16\]

Jonask
 one year ago
Best ResponseYou've already chosen the best response.1\[f(0)=4(f(2)8)1=4f(2)161=4f(2)17\]

Jonask
 one year ago
Best ResponseYou've already chosen the best response.1is f always of the from\[ax^2+bx+c\]

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.0No, it's a polynomial. It can be in that form, but we're not sure.

Jonask
 one year ago
Best ResponseYou've already chosen the best response.1so far we see \[f(10)+11^3=2f(11)\] \[f(9)+10^3=2f(10)\]  \[f(10)=f(9)2f(11)+11^310^3\]

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.0I think that it must be in the form \(ax^3 + bx^2 + cx + d\)

Jonask
 one year ago
Best ResponseYou've already chosen the best response.1we need a relation between f(9) and f(11)

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.0\[f(9) = 2f(10)  1000\]\[f(10) = 2f(11)  1331\]\[\iff f(9) = 2(f(11)  1331 )  1000\]

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.0\[f(9) = 2f(11)  2662  1000\]

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.0That's the relation.

Jonask
 one year ago
Best ResponseYou've already chosen the best response.1isnt this the solution then

Jonask
 one year ago
Best ResponseYou've already chosen the best response.1since \[f(9)2f(11)=3662\] \[f(10)=3662+11^310^3\]

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.0But it's an integer between 0 and 999.

Jonask
 one year ago
Best ResponseYou've already chosen the best response.1okay so we found a relationship between numbers 2 units away from each other x1 and x+1 \[\color{blue}{f(x1)+x^3=2f(x).......... f(x)+(1+x)^3=2f(1+x)}\] \[f(x1)+x^3=4f(x+1)+2(x+1)^3\]

Jonask
 one year ago
Best ResponseYou've already chosen the best response.1\[f(9)4f(11)=2(11)^310^3\]

Jonask
 one year ago
Best ResponseYou've already chosen the best response.1earlier we used 2 not 4

sauravshakya
 one year ago
Best ResponseYou've already chosen the best response.3Let f(x)=a+bx+cx^2+dx^3 NOTE: f(x) must be a third degree polynomial

sauravshakya
 one year ago
Best ResponseYou've already chosen the best response.3Now, f(x)+(x+1)^3 =2f(x+1)

Jonask
 one year ago
Best ResponseYou've already chosen the best response.1\[\huge f(10)=f(9)2f(11)+11^310^3=???\]

sauravshakya
 one year ago
Best ResponseYou've already chosen the best response.3use it to find a,b,c and d

sauravshakya
 one year ago
Best ResponseYou've already chosen the best response.3u will get a=13 b=9 c=3 d=1

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.0Equating coefficients

sauravshakya
 one year ago
Best ResponseYou've already chosen the best response.3now, once u know f(x) u can find f(10)

Jonask
 one year ago
Best ResponseYou've already chosen the best response.1help me i dont get where you get the coeeffients from

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.0@Jonask a technique.\[ax + by = 2x + 3y\]means\[a=2,b=3\]

sauravshakya
 one year ago
Best ResponseYou've already chosen the best response.3f(x)+(x+1)^3 =2f(x+1) a+bx+cx^2+dx^3 +x^3+3x^2+3x+1 = 2{a+b(x+1) +c(x+1)^2 +d(x+1)^3

sauravshakya
 one year ago
Best ResponseYou've already chosen the best response.3can u continue from here?

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.0\[f(10) = 10^3  3(10)^2 +9(10) 13 = 1000  300 + 90  13 \\ = 777 \]

Jonask
 one year ago
Best ResponseYou've already chosen the best response.1\[\huge \color{green}{THANKS}\]
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