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hi , The solution of this is simple
x^5 = 5y^3 - 4z
y^5 = 5z^3 - 4x
z^5 = 5x^3 - 4y
Since all three equations are rotational
like
x=y+z
y=x+z
z=x+y
That is they rotate from preceding equation
This implies
x=y=z
So just place y & z with x from any of the equation
x^5 = 5x^3 - 4x
=>x^5-5x^3 + 4x=0
=>x(x^4-5x^2 + 4)
=>x((x^2 -4)(x^2 -1))
=>Hence now it is easy I suppose
x=-2,-1,0,1,2 =y=z
You can take any value at the time and can verify
I think there is no integer solution other then 1
x^2+2^(x-1/x)-2^(2-1/x)
=>x^2=2^2*2^(-1/x)-2^x*2^(1/x)
on solving it gives
X^2=2^x-2^(x-1/x)/2^1/x
Since the denominator is 2^1/x so other than 1 it would be non rational value..........
Lets do it step by step instead of using formula...
Since
In 2001 it would be
A2001=A2000-A2000*r/100
Hence A2001=A2000(1-r/100)
Similiarly A2002=A2001(1-r/100)
A2003=A2002(1-r/100)
A2004=A2003(1-r/100)=A2002(1-r/100)^2=A2001(1-r/100)^3=A2000(1-r/100)^4
Hence A2004=A2000(1-r/100)^4
This is from where actual formula arises..............
Benefit of doing step by step is like if rate changes every year.........r1,r2,r3,r4
Formula would be
A2004=A2000(1-r1/100)(1-r2/100)(1-r3/100)(1-r4/100)
HI Everyone...........
You have 12 coins one of them is defective by weight,all are identical...(not known heavier or lighter)....
Using weight balance 3 times only can you identify defective coin...........
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