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Algebra

Blazing goIITian

 Joined: 19 Mar 2012 Post: 421
22 Aug 2012 23:26:10 IST
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5
250
plz solve ........
Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Algebra

4^x+1 + 4 ^ 1-x = 10 . find x.

Blazing goIITian

Joined: 19 Mar 2012
Posts: 421
22 Aug 2012 23:38:27 IST
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guyz plz solve this........

Blazing goIITian

Joined: 19 Mar 2012
Posts: 421
22 Aug 2012 23:52:34 IST
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???????????????????????????????

Hot goIITian

Joined: 10 Aug 2011
Posts: 103
23 Aug 2012 12:19:57 IST
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4^x+1+4^1-x = 10

4^x + 4^1-x = 9

4^x + 4.4^-x = 9

4^x + 4/4^x = 9

4^2x + 4 = 9.4^x

let 4^x = a

a^2 + 4 = 9a

a^2 -9a + 4 = 0

solve this quadratic eq. and find value of a

then put 4^x in place of a and solve for x.............

Blazing goIITian

Joined: 6 May 2007
Posts: 1041
23 Aug 2012 17:39:01 IST
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$\\4^{x+1} + 4 ^ {1-x} = 10\\\Rightarrow 4^x+4^{-x}=\frac{5}{2}\\Let\ 4^x=t\\ \\ \Rightarrow t+\frac{1}{t}=\frac{5}{2}\\ \\ \Rightarrow t=\frac{1}{2}, t=2\\ \\ \Rightarrow 2^{2x}=2^{-1}, 2^{2x}=2^1\\ \\ \Rightarrow x=\frac{-1}{2}, x=\frac{1}{2}$

Blazing goIITian

Joined: 19 Mar 2012
Posts: 421
24 Aug 2012 19:27:15 IST
0 people liked this

thankss

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