Algebra

reddevil_2009's Avatar
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14 Nov 2008 12:01:05 IST
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Find x
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Algebra

If  the  third term in expansion of   is 1000,then find x.......



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Sagar Saxena's Avatar

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14 Nov 2008 13:16:05 IST
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here the answer is x = 100;if there is ne problem in solving the question than nudge me ,i will provide you the coplete solution

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14 Nov 2008 13:27:09 IST
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take log [10] x = y...u wil get a quadratic in y...one root is 2..y=2..x=100..
Gaurav |spideyunlimited| Ragtah's Avatar

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14 Nov 2008 13:29:26 IST
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5C2. (1/x)^3 ( x^[log_10 x] )^2 = 1000
(1/x)^3 ( x^[log_10 x] )^2 = 100
x^(-3) . x^(2.[log_10 x] ) = 100
x^(-3) . x^(log_10 x^2) = 100
x^[-3 + log_10 x^2] = 100
log_x 100 = -3 + log_10 x^2
3 = 2 (log_10 x - log_x 10)
take log_10 x = A, then log_x 10 = 1/A
Solve the quadratic you get,
and the result is A = 2.
So log_10 x = A = 2
x = 100
ganapathi  1810's Avatar

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14 Nov 2008 14:15:34 IST
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let   x=10^y


(10(-y)  +   10(y^2) )5


5c2 * (10(y^2) )2  * (10(-y) )    =1000


we   got   quadritic  equation


2 y2  -  3y  -2  =0


y =2,  -1/2




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