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Also 'b' is the geometric mean between 'a' and 'c'<br>
Also 'b' is the geometric mean between 'a' and 'c'<br>
That is b = <math>\sqrt{ac}</math><br>
That is b = <math>\sqrt{ac}</math><br>
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We also write this as <math>b^{2}</math> = ac.<br>
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We also write this as <math>b^{2}</math> = ac.-------->2<br>
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Now substitute
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Now substitute thia value In equation 1,<br>
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2ab = ac + bc<br>
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Take common in right hand side ( c is common )<br>
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2ab = c(a + b)<br>
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Divide both side by (a + b),<br>
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<math>\frac{2ab} {a + b}</math><br>
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Hence 'c' is the harmonic between 'a' and 'b'.