Question

4^X^2+128=3^(1-X^2)*12^X^2

Answer 1

Ответ:

Объяснение:

4^X^2+2^7=3/3^X^2*12^X^2

4^X^2+2^7=3/3^X^2*3^X^2*4^X^2

4^X^2+2^7=3*4^X^2

-2*4^X^2=-2^7

4^X^2=2^6

4^X^2=4^3

x^2=3

x= √3  x= -√3

Answer 2

To solve the equation 4^(X^2) + 128 = 3^(1 - X^2) * 12^(X^2), we'll first attempt to simplify it by recognizing that 12 can be expressed as 4 * 3:

4^(X^2) + 128 = 3^(1 - X^2) * (4 * 3)^(X^2)

Now, let's express 128 as a power of 2:

4^(X^2) + 2^7 = 3^(1 - X^2) * (4 * 3)^(X^2)

Now, we can rewrite 2^7 as 4^2:

4^(X^2) + 4^2 = 3^(1 - X^2) * (4 * 3)^(X^2)

Using the properties of exponents, (4 * 3)^(X^2) can be simplified as 4^(X^2) * 3^(X^2):

4^(X^2) + 4^2 = 3^(1 - X^2) * 4^(X^2) * 3^(X^2)

Now, we can cancel out the common factor of 4^(X^2) from both sides:

4^2 = 3^(1 - X^2) * 3^(X^2)

Next, use the property that a^(m) * a^(n) = a^(m + n):

4^2 = 3^(1 - X^2 + X^2)

Simplify the exponents:

16 = 3^1

Since 3^1 equals 3, we get:

16 = 3

The equation is a contradiction, and there are no real solutions for X that satisfy the original equation. The reason for this is that the left-hand side of the equation (16) is always greater than the right-hand side (3). Therefore, there are no solutions for X that make the equation valid.