Question

Mean proportional between x^3y & xy^3

Answer 1

Answer:

x²y²

Step-by-step explanation:

Given :-

x³y & xy³

To find :-

Find the mean Proportional between them ?

Solution :-

Method -1:-

Given expressions are x³y & xy³

Let the Mean Proportional between them be A

So, x³y : A : : A : xy³

Product of means = A×A = A²

Product of extremes = x³y×xy³

=> (x³×x)×(y×y³)

=> x⁴ y⁴

(Since (a^m)^n = a^mn)

In Proportion ,The product of means is equal to The product of extremes

=> A² = x⁴y⁴

=> A = √(x⁴y⁴)

=> A =√[(x²y²)²]

=> A = x²y²

The Mean Proportional = x²y²

Method -2:-

The Mean Proportional between the two numbers a and b is √ab.

We have, a = x³y and b=xy³

On applying this formula then

Mean Proportional between them

=> √(x³y×xy³)

=> √(x⁴y⁴)

=> √[(x²y²)²]

=> x²y²

The Mean Proportional = x²y²

Answer:-

The Mean Proportional between x³y and xy³ is x²y²

Used formulae:-

• In Proportion ,The product of means is equal to The product of extremes

• (a^m)^n = a^mn

• The Mean Proportional between the two numbers a and b is √ab.

Points to know:-

• Equality of ratios is called Proportion.

• The symbol for Proportion is ': : ' and this is read as "is as".

• If a,b,c,d are in Proportion then a:b::c:d => bc = ad.