Question

Find the sum of two numbers whose geometric mean is 6 and third proportional is 20.25. Pls ans fast I'll mark as brainliest. No spams pls​

Answer 1

Step-by-step explanation:

Hope it helps you in your learning process.

Answer 2

The sum of two numbers is 13.

Step-by-step explanation:

Let x be the first number and y be the second number.

Geometric mean of two numbers a and b is

$GM=\sqrt{ab}$

Geometric mean of two numbers x and y is

$GM=\sqrt{xy}$

It is given that geometric mean of two number is 6.

$6=\sqrt{xy}$

Taking square on both sides.

$36=xy$

$\dfrac{36}{y}=x$             .... (1)

If $\frac{a}{b}=\frac{b}{c}$, then c is known as third proportional.

It is given that third proportional of x and y is 20.25.

$\frac{x}{y}=\frac{y}{20.25}$

Multiply both sides by y.

$x=\frac{y^2}{20.25}$           .... (2)

From (1) and (2) we get

$\frac{y^2}{20.25}=\dfrac{36}{y}$

On cross multiplication we get

$y^3=36\times 20.25$

$y^3=729$

$y^3=9^3$

On comparing both sides we get

$y=9$

Substitute y=9 in equation (1).

$x=\dfrac{36}{9}=4$

Therefore, the value of x is 4.

The sum of x and y is

$x+y=4+9=13$

Therefore, the sum of two numbers is 13.

#Learn more

What is the geometric mean of 4 and 25.

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