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desiguy
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if 7^8y+2 = 196z^2, then 7^4y - 2^z = ? 0 sqrt7 7 28 49 the 08 Nov 2005, 20:53
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if 7^8y+2 = 196z^2, then 7^4y - 2^z = ?

0
sqrt7
7
28
49

the 7 is raised to the entire 8y+2.



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if 7^8y+2 = 196z^2, then 7^4y - 2^z = ? 0 sqrt7 7 28 49 the 08 Nov 2005, 22:28
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7^(8y+2)=7^8y*7^2=7^2.2^2z^2

(7^4y)^2=2^2z^2

sqrt the above

you get 7^4y=2z

7^4y-2^z < I am not sure...is 2z? if it is 2z then ans is 0....
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if 7^8y+2 = 196z^2, then 7^4y - 2^z = ? 0 sqrt7 7 28 49 the 08 Nov 2005, 22:34
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fresinha12
7^(8y+2)=7^8y*7^2=7^2.2^2z^2

(7^4y)^2=2^2z^2

sqrt the above

you get 7^4y=2z

7^4y-2^z < I am not sure...is 2z? if it is 2z then ans is 0....
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yeah, the same confusion here ...dunno if the question contains typo
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if 7^8y+2 = 196z^2, then 7^4y - 2^z = ? 0 sqrt7 7 28 49 the 09 Nov 2005, 06:36
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actually there is one little typo (sorry i was typing last last nite)...

the last expression should be 7^4y - 2z

Otherwise, the question is correct.

FYI, this is a question from the Mgmat 750 course that one of my friends showed me.
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if 7^8y+2 = 196z^2, then 7^4y - 2^z = ? 0 sqrt7 7 28 49 the 09 Nov 2005, 07:04
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desiguy
if 7^8y+2 = 196z^2, then 7^4y - 2z = ?

0
sqrt7
7
28
49

the 7 is raised to the entire 8y+2.
Show more


7^(8y+2)= 196z^2 ---> 7^(8y)= 196/49 *z^2= 4*z^2= (2z)^2

7^(8y)= (2z)^2
There're only two solutions:
1. 7^ (8y)= (2z)^2= 1, thus y=0 and z = 1/2
we have 7^4y - 2z = 7^0 - 2(1/2) = 1-1 = 0
2. 2z must be 7, otherwise RHS is always the power of 7 and other numbers rather than 7 and RHS can't be equal to LHS ----> z=7/2
RHS= 7^2 ---> LHS= 7^2 ---> 8y= 2 ---> y=1/4
---->7^4y - 2z = 7^(4*1/4) - 2*7/2= 7-7 =0
A it is.
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if 7^8y+2 = 196z^2, then 7^4y - 2^z = ? 0 sqrt7 7 28 49 the 09 Nov 2005, 07:37
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I got A.

7^(8y+2) =196z^2
or, 7^8y* 49 =196z^2

or 7^8y =4z^2

or 7^4y =2z,

then, 7^4y - 2z = 0
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if 7^8y+2 = 196z^2, then 7^4y - 2^z = ? 0 sqrt7 7 28 49 the 09 Nov 2005, 07:43
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desiguy
if 7^8y+2 = 196z^2, then 7^4y - 2^z = ?

0
sqrt7
7
28
49

the 7 is raised to the entire 8y+2.
Show more


A slightly different approach:

7^8y+2=196z^2------> 7^8y*7^2=49*2z^2
cancel out the 7^2 and 49 we get -----> 7^8y=2z^2
set the equation equal to 0 ------> 7^4y^2-2z^2=0
Reverse foil ----> (7^4y+2z)(7^4y-2z)=0
(7^4y-2z) must equal 0.
Choose A.
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if 7^8y+2 = 196z^2, then 7^4y - 2^z = ? 0 sqrt7 7 28 49 the 09 Nov 2005, 08:02
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nakib77
I got A.

7^(8y+2) =196z^2
or, 7^8y* 49 =196z^2

or 7^8y =4z^2

or 7^4y =2z,

then, 7^4y - 2z = 0
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consider the bold part: it can also be 7^4y= -2z . This is exactly what is pointed out by Matt's approach : ( 7^4y+2z) ( 7^4y-2z) = 0 (1)

my approach negected this point also ....
But, Matt, equation (1) has two solutions : it can also be that 7^4y+2z= 0---> y= 0 and z=-1/2 ...then 7^4y-2z= 1+1 = 2



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