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Algebra

Blazing goIITian

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18 May 2011 08:21:15 IST

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863

if xyz = 1 and x + (1/z) = 5 and y + (1/x) = 29 find the value of z + (1/x).

None

if xyz = 1 and x + (1/z) = 5 and y + (1/x) = 29 find the value of z + (1/x).

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Comments (9)

varun ganesh

Scorching goIITian

Joined: 17 Jul 2010

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18 May 2011 10:52:52 IST

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is it z+(1/y)? to be evaluated...?

NugoRama

Blazing goIITian

Joined: 11 Mar 2009

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18 May 2011 11:08:25 IST

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Simple.

xyz = 1, this implies y = 1/xz ....(1)

y + 1/x = 29 ......(2)

1/xz + 1/x = 29

1/x( 1/z + 1 ) = 29......(3)

x + 1/z = 5, this implies 1/z = 5 -x

Put the value of 1/z in (3)

1/x ( 5 - x + 1) = 29

6 - x = 29x

30x = 6

x = 1/5

Put the value of x in (2)

y + 5 = 29

y = 24

Put the value of x and y in (1)

1/5.24.z = 1

z = 5/24

Hence, x = 1/5, y = 24 and z = 5/24

Now, z + 1/x = 5/24 + 5 = 125/24. Answer.

varun ganesh

Scorching goIITian

Joined: 17 Jul 2010

Posts: 299

18 May 2011 11:30:29 IST

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hey hey its much simple observation but his one's a little more tricky......

z +(1/y) be equal to 'K"

then multiplying the last given two relations with K, we get.....

29x5xk=(x+1/z)(y+1/x)(z+1/y)

=x+y+z+1/xy+1/yz+1/zx

=x+y+z+1/x+1/y+1/z

=(x+1/z)+(y+1/x)+(z+1/y)

=5+29+K

29x5xK=5+29+K

solvig this we get what is asked-----"K"and K=17/72

now we get all three i.e. z+1/y=17/72

soving all three------ z=5/24, x=1/5, y=24

z+1/x=125/24

kushashwa ravi shrimali

New kid on the Block

Joined: 18 May 2011

Posts: 11

18 May 2011 15:14:49 IST

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I would like to say that this is a tricky question. your solution of this question is following pls not it down as i am writing it in steps.

STEP 1:

Given that : xyz = 1

y = 1/xz

STEP 2: Now putting the value of y from the step 1 in the equation given we wil lget:

y + 1/x = 29

1/xz + 1/x = 29

taking 1/x as common we will get:

1/x ( 1/z + 1 ) = 29

STEP 3: Given that :

x + 1/z = 5

1/z = 5 - x

STEP 4: Putting the value of 1/z (that we got in step 3) in the equation:

1/x ( 1/z + 1) = 29

1/x ( 5-x + 1) = 29

1/x ( 6-x ) = 29

6 - x = 29x

6 = 29x + x

6 = 30x

1/5 = x

STEP 5: putting the value of x in the equation :

x + 1/z = 5

1/5 + 1/z = 5

1/z = 5 - 1/5

1/z = 24/5

z = 5/24

STEP 6: FINDING THE SOLUTION AT LAST BY PUTTING THE VALUE OF x AND z in the equation given

z + 1/x

5/24 + 5

125/24

HENCE THE ANSWER IS 125/24

Hope you have understood the solution. If not or yes than please reply to my answer.

Thanks

Inferno

Blazing goIITian

Joined: 19 Apr 2010

Posts: 359

18 May 2011 19:16:47 IST

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Same thing is being written three times. Oh!! Someone please put it in Hindi as well. The third guy has copied the entire thing from the first guy.

NugoRama

Blazing goIITian

Joined: 11 Mar 2009

Posts: 5517

18 May 2011 19:28:16 IST

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First post dude. He's a 'new kid on the block'... Happens.

Inferno

Blazing goIITian

Joined: 19 Apr 2010

Posts: 359

18 May 2011 20:00:14 IST

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Oh!! Sorry man. I take my words back. But you should at least check what others have written.

kushashwa ravi shrimali

New kid on the Block

Joined: 18 May 2011

Posts: 11

19 May 2011 07:24:18 IST

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sorry for that i didn't knew that but that is why i had given stars to NUO RAMA for his gr8 answer or soulution. i m actually in 8th class so sorry;.

hemang

Blazing goIITian

Joined: 27 Dec 2010

Posts: 1474

19 May 2011 10:50:17 IST

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we can write x+(1/z) as (1/yz) + (1/z) solving this we get(1+y)/yz = 5 ................(1)

now from the second equation we get y + yz = 29

or, yz = 29-y putting it in (1) we get (1+y) = 5(29-y)

or, 1+y = 145 - 5y6y = 144or, y = 24now again putting it in (1) we get 25 = 120z

or, z = 5/24so x = 1/yz or, x = 1/5 notice that this fulfills the requirement xyz = 1so now z + 1/x = z + zy = 5/24 + (5/24)(1/5) = 5/24 + 1/24 = 1/4 answer.

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