Answer:
Let's solve the equation \(x \cdot \sqrt{x} = (x\sqrt{x})^2\) to identify the value of \(x\).
Starting with the given equation:
\[x \cdot \sqrt{x} = (x\sqrt{x})^2\]
First, square the term on the right side:
\[x \cdot \sqrt{x} = x^2 \cdot x\]
Combine the terms on the right side:
\[x \cdot \sqrt{x} = x^3\]
Now, divide both sides of the equation by \(x\) to solve for \(\sqrt{x}\):
\[\sqrt{x} = x^2\]
Square both sides to eliminate the square root:
\[x = x^4\]
Now, if \(x\) is not zero, we can simplify by dividing both sides by \(x\):
\[1 = x^3\]
So, the value of \(x\) is 1.
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Answer:
Let's solve the equation \(x \cdot \sqrt{x} = (x\sqrt{x})^2\) to identify the value of \(x\).
Starting with the given equation:
\[x \cdot \sqrt{x} = (x\sqrt{x})^2\]
First, square the term on the right side:
\[x \cdot \sqrt{x} = x^2 \cdot x\]
Combine the terms on the right side:
\[x \cdot \sqrt{x} = x^3\]
Now, divide both sides of the equation by \(x\) to solve for \(\sqrt{x}\):
\[\sqrt{x} = x^2\]
Square both sides to eliminate the square root:
\[x = x^4\]
Now, if \(x\) is not zero, we can simplify by dividing both sides by \(x\):
\[1 = x^3\]
So, the value of \(x\) is 1.