The Power of three

Algebra Level 4

$\large(4^x+2^x-6)^3=(2^x-4)^3+(4^x-2)^3$

Find the sum of all solutions, such that the above equation satisfies.

1 solution

Tanishq Varshney
Oct 29, 2015

$a=4^x-2$ and $b=2^x-4$

$(a+b)^3=a^3+b^3+3ab(a+b)$

we get

$3(4^x-2)(2^x-4)(4^x+2^x-6)=0$

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

$* 2^x=4 \rightarrow x=2$

$*(2^x+3)(2^x-2)=0 \rightarrow x=1;2^x \neq -3$

Thus sum of values $=1+2+1/2=\boxed{3.5}$

I Did same.

Dev Sharma - 5 years, 7 months ago

I also did same.

Kushagra Sahni - 5 years, 7 months ago