Question

Solve the following equation.
$2^x+2^y=20,x+y=6$.

• A. $x=2,y=4$
• B. $x=3,y=3$
• C. $x=3,y=2$
• D. $x=0,y=2$

Answer 1

The correct option is A $x=2,y=4$

Given $x+y=6$

$2^x+2^y=20\Rightarrow 2^x+2^{6-x}=20$

Multiplying the Equation by $2^x$

$2^{2x}-{20.2}^x+2^6=0\Rightarrow 2^{2x}-{20.2}^x+64=0\Rightarrow (2^x-{16.2}^x-{4.2}^x+64)=0\Rightarrow (2^x-16)(2^x-4)=0\Rightarrow 2^x=16or{2}^x=4\Rightarrow x=4orx=2$

Since $x+y=6\Rightarrow y=2or4$