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Find π¦ given the geometric mean between two and π¦ is 10.
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First letβs recall the definition of the geometric mean.
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The geometric mean of two positive numbers π and π is the square root of their product, ππ.
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In this question, weβve been told that the geometric mean is 10.
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Weβve also been told one of the numbers is two.
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And we want to work backwards in order to find the other.
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So using the information in the question and our definition of the geometric mean, we can write down that the square root of the product of the two numbers two π¦ is equal to 10.
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This gives us an equation that we can solve in order to find the value of π¦.
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As there is a square root on the left-hand side of the equation, the first step is to square both sides.
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This cancels out the square root and gives two π¦ is equal to 10 squared, which is 100.
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Finally, to find the value of π¦, we need to divide both sides of this equation by two.
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This gives the solution to the problem: π¦ is equal to 50.