Question

The sum of all possible values of \(x\) satisfying the equation \(2^{4x^2} - 2^{2x^2+x+16} + 2^{2x+30} = 0\), is

• A. \(\frac{5}{2}\)
• B. \(\frac{1}{2}\)
• C. 3
• D. \(\frac{3}{2}\)

Answer 1

The Correct Option is B

Given That,
\(2^{4x^2} - 2^{2x^2+x+16} + 2^{2x+30} = 0\)
\(⇒ (2^{2x^2})^2-2^{2x^2}.2^{x+15}.2^1+(2^{x+15})^2=0\)
\(⇒ (2^{2x^2}-2^{x+15})^2=0\)
\(⇒ 2^{2x^2}-2^{x+15}=0\)
\(⇒ 2^{2x^2}=2^{x+15}\)
\(⇒ 2x^2=x+15\)
\(⇒ 2x^2-x-15=0\)
\(⇒ (2x+5)(x-3)=0\)
\(⇒ x=-\frac 52, \ 3\)
Now, the of possible values = \(-\frac 52+3 = \frac 12\)

So, the correct option is (B): \(\frac 12\)