Question

If ${\left(4\right)}^{x+y}=1$ and ${\left(4\right)}^{x-y}=4$, then the value of $x$ and $y$ will be respectively

• A. $\frac{1}{2}$ and $-\frac{1}{2}$
• B. $\frac{1}{2}$ and $\frac{1}{2}$
• C. $-\frac{1}{2}$ and $-\frac{1}{2}$
• D. $-\frac{1}{2}$ and $\frac{1}{2}$

Answer 1

The correct option is A $\frac{1}{2}$ and $-\frac{1}{2}$

$4^{x+y}=1$

$\Rightarrow 4^{x+y}=4^0$ .......... (1)

$4^{x-y}=4$

$\Rightarrow 4^{x-y}=4^1$ ........... (2)

We know that if both sides have the same number, the power of number is also same

Then from (1) and (2), we get

$x+y=0$ ............ (3)

$x-y=1$ ........... (4)

$(x+y)+(x-y)=0+1$

$\Rightarrow x+y+x-y=1$

$\Rightarrow 2x=1$

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

$\Rightarrow \frac{1}{2}-y=1$

$\Rightarrow y=\frac{1}{2}-1=-\frac{1}{2}$

Then $x=\frac{1}{2}$ and $y=-\frac{1}{2}$