Answer :
Answer:
We are told that an integer (let's call it "x") multiplied by a fraction, then equals the reciprocal of itself. Here's how we can find "x":
Step-by-step explanation:
Reciprocal of x: The reciprocal of x is simply 1/x.
Multiply by -12/-9: The problem states "x multiplied by -12/-9". This is the same as multiplying by 4/3 (since dividing by a negative number is the same as multiplying by its inverse).
So, according to the problem:
x * (4/3) = 1/x
Solve for x: To solve for x, we can multiply both sides of the equation by x:
x^2 * (4/3) = 1
Simplify:
(4/3) * x^2 = 1
x^2 = 3/4
Take the Square Root (be cautious): We can take the square root of both sides to find x. However, be aware that squaring a number can result in both positive and negative versions of the root.
x = ±√(3/4)
Taking the square root of 3/4 gives us:
Positive square root: x = √(3/4) ≈ 0.866 (approximately)
Negative square root: x = -√(3/4) ≈ -0.866 (approximately)
Checking Solutions:
The problem asks for an integer solution (a whole number). Neither √(3/4) nor -√(3/4) are integers. Therefore, there are NO integer solutions for "x" that satisfy the given conditions.
Answer: There are NO integer solutions for this problem.
