2^ (2x) + 2^ (x+2) - 12=0

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Solve for x

Answer

Question

Avery Moore

Mathematics

18 December, 08:09

2^ (2x) + 2^ (x+2) - 12=0

|

Solve for x

Answer

+1

Answers (1)

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Rishi Eaton · Answer 1

2^ (2x) = (2^x) ^2;

2^ (x+2) = (2^x) * 4;

Let be 2^x = y > 0;

y^2 + 4y - 12 = 0;

a = 1;

b = 4;

c = - 12;

b^2 - 4ac = 16 + 48 = 64;

y1 = ( - 4 + 8) / 2 = 2 > 0 (correct);

y2 = ( - 4 - 8) / 2 = - 6 > 0 (false);

Then, 2^x = 2;

x = 1.

2^ (2x) + 2^ (x+2) - 12=0|Solve for xAnswer

2^ (2x) + 2^ (x+2) - 12=0

|

Solve for x

Answer