Question

Solve 6ˣ² = 12x − 20.

a) 1/4+i √21/3
b) 1/4-i √21/3
c) 1/4+i √39/3
d) 1/4-i √21/3

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Answer 1

To solve the given equation 6ˣ² = 12x - 20, we can use the quadratic formula. The solutions to the equation are (12 + √624) / 12 and (12 - √624) / 12.

Step-by-step explanation:

This expression is a quadratic equation of the form ax² + bx + c = 0, where the constants are a = 6, b = -12, and c = -20. To solve this equation, we can use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Substituting the values for a, b, and c, we have: x = (-(-12) ± √((-12)² - 4(6)(-20))) / (2(6)).

Simplifying the equation further, we get: x = (12 ± √(144 + 480)) / 12.

This can be simplified to: x = (12 ± √624) / 12.

Therefore, the solutions to the equation are: x = (12 + √624) / 12 and x = (12 - √624) / 12.