The mean proportional of (a+b)(a-b)³,(a+b)³ (a-b) is:

Given: ​

​(a + b)(a - b)³, (a + b)³ (a - b) 

if a , b are in ratio.

Mean proportion = $$\sqrt{ab}$$   

$$\text{Let mean proportion} = x \\[10pt]\frac{(a + b)(a - b)^3}{x} = \frac{x}{(a + b)^3 (a - b)} \\[10pt]\Rightarrow x^2 = (a + b)^4 \times (a - b)^4 \\[10pt]\Rightarrow x = \sqrt{(a + b)^4 \times (a - b)^4} \\[10pt]\Rightarrow x = (a + b)^2 (a - b)^2$$​​

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