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solve the following equation by systematic method 3m^2+2=M^2- 7
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3m^2 - M^2 = -7 - 2
Now, we need to combine like terms on the left side of the equation.
3m^2 - M^2 = -9
Next, we can factor out a common factor of m^2:
m^2(3 - 1) = -9
Simplifying further:
2m^2 = -9
To solve for m,
we need to isolate the variable. We can divide both sides of the equation by 2:
m^2 = -9/2
However, since we're solving a quadratic equation, we need to determine if there are any solutions for m. To do this, we need to check the discriminant, which is the expression under the square root in the quadratic formula (b^2 - 4ac). In this case, a = 1, b = 0, and c = -9/2:
b^2 - 4ac = 0^2 - 4(1)(-9/2) = 0 + 18 = 18
The discriminant is positive (greater than 0), which means there are two distinct real solutions for m.
Let's use the square root property to find the solutions.
m = ± √(-9/2)
Since the expression under the square root is negative, it means that the solutions are imaginary.
Therefore, the equation 3m^2 + 2 = M^2 - 7 does not have any real solutions for m.