Question

solve 4^x+1+4^1-x =10

Answer 1

Answer:

x is 1by2 or minus 1by 2

Step-by-step explanation:

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Answer 2

The values of x is   $-\frac{1}{2}$   and  $\frac{1}{2}$ .

Step-by-step explanation:

Given:

The equation $4^{x+1} + 4^{1-x} =10$.

To Find:

The values of x.

Solution:

As given-the equation $4^{x+1} + 4^{1-x} =10$.

$4^{x+1} + 4^{1-x} =10$

$4^{x} .4 + 4.4^{-x} =10$

$4.4^{x} +\frac{4}{4^{x} } =10$

$\frac{4.(4^{x} )^{2}+4 }{4^{x} } =10$

$4.(4^{x} )^{2} +4 =10. 4^{x}$

$4.(4^{x} )^{2} -10. 4^{x} +4 =0$

Putting $4^{x} =p$

$4p^{2} -10p+4=0$

$4p^{2} -8p -2p+4=0$

$4p(p-2) -2(p-2) =0$

$(4p-2) (p-2)=0$

$p=\frac{1}{2} \ and \ p= 2$

Considering  $p=\frac{1}{2}$.

$p=\frac{1}{2}$

Putting $p=4^{x}$.

$4^{x} =\frac{1}{2}$

$2^{2x} =2^{-1}$

$2x=-1$

$x= - \frac{1}{2}$

Considering $p=2$.

$p=2$

Putting $p=4^{x}$.

$4^{x} =2$

$2^{2x} =2^{1}$

$2x=1$

$x= \frac{1}{2}$

Thus, The values of x is $-\frac{1}{2}$   and $\frac{1}{2}$ .

Correct Question

Solve $4^{x+1} + 4^{1-x} =10$.