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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

sauravshakyaBest ResponseYou've already chosen the best response.3
f(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
 one year ago

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

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

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