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Albert1
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$x,y,z,w $ are all integers
if (1):$ w>x>y>z$
and(2) :$2^w+2^x+2^y+2^z=1288\dfrac {1}{4} $
find $x,y,z,w$
if (1):$ w>x>y>z$
and(2) :$2^w+2^x+2^y+2^z=1288\dfrac {1}{4} $
find $x,y,z,w$
Albert said:$x,y,z,w $ are all integers
if (1):$ w>x>y>z$
and(2) :$2^w+2^x+2^y+2^z=1288\dfrac {1}{4} $
find $x,y,z,w$
mente oscura said:Hello.
[tex]z=-2[/tex]
[tex]2^w+2^x+2^y=1288=2^3*161[/tex]
[tex]y=3[/tex]
[tex]2^{w-3}+2^{x-3}=161-1=160=2^5*5[/tex]
[tex]x-3=5 \rightarrow{} x=8[/tex]
[tex]2^{w-8}=5-1=2^2 \rightarrow{} w=10[/tex]
Therefore:
[tex]z=-2, \ / \ y=3, \ / \ x=8, \ / \ w=10[/tex]
Regards.
Albert said:$x,y,z,w $ are all integers
if (1):$ w>x>y>z$
and(2) :$2^w+2^x+2^y+2^z=1288\dfrac {1}{4} $
find $x,y,z,w$
"Integer solutions" refers to a set of whole number values that satisfy a given mathematical equation or inequality. These values can be positive, negative, or zero.
To find all integer solutions, you can use techniques such as substitution, elimination, or graphing. These methods involve manipulating the given equation or system of equations to isolate the variable and solve for its value.
Yes, there may be limitations depending on the complexity of the equation or the number of variables involved. In some cases, it may not be possible to find all integer solutions or the process may be too time-consuming.
Yes, the solutions can be verified by substituting them back into the original equation and checking if they satisfy the equation. This is an important step to ensure that all solutions have been found.
Finding all integer solutions can be useful in various fields such as engineering, economics, and computer science. It can help in solving optimization problems, modeling real-world situations, and analyzing data.