Question : The mean proportional of $(a+b)(a-b)^3,(a+b)^3(a-b)$ is:
Option 1: $(a+b)^2(a–b)^2$
Option 2: $(a+b)^2(a–b)$
Option 3: $(a+b)(a–b)^2$
Option 4: $a^2-b^2$
Answer (1)
16th Jan, 2024
Correct Answer: $(a+b)^2(a–b)^2$
Solution :
Let the mean proportion of $(a+b)(a-b)^3,(a+b)^3(a-b)$ be $x$.
Mean proportion of $A$ and $B$ = $\sqrt{A×B}$
⇒ $x=\sqrt{ (a+b)(a-b)^3 \times (a+b)^3(a-b)}$
⇒ $x = \sqrt{(a+b)^4 (a-b)^4}$
⇒ $x = (a+b)^2(a-b)^2$
Hence, the correct answer is $(a+b)^2(a-b)^2$.
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