Question

Find the mean proportional between 81 and 144.​

Answer 1

Step-by-step explanation:

Let the required number be x&y.

∴14is the mean proportional between x&y.

Then,

x/18=18/y

⇒xy=18×18=324

⇒x=324/y ..(1)

And given that, 144 is the third proportional to x&y.

Then, x:y :: y:144

i.e. x/y=y/144

⇒y^2=144x ..(2)

Putting the value of x by equation (1) to (2) and we get,

⇒y^2=144× 324/y

⇒y^3=144×324

⇒y^3=2×2×2×2×3×3×2×3×3×2×3×3

⇒y^3=36×36×36

⇒y^3=36^3

⇒y=36

Put the value of y in equation (1), and we get

x=324/36

x=9

Hence, this is the answer.

Answer 2

Step-by-step explanation:

Step-by-step explanation:

Let the required number be x&y.

∴14is the mean proportional between x&y.

Then,

x/18=18/y

⇒xy=18×18=324

⇒x=324/y ..(1)

And given that, 144 is the third proportional to x&y.

Then, x:y :: y:144

i.e. x/y=y/144

⇒y^2=144x ..(2)

Putting the value of x by equation (1) to (2) and we get,

⇒y^2=144× 324/y

⇒y^3=144×324

⇒y^3=2×2×2×2×3×3×2×3×3×2×3×3

⇒y^3=36×36×36

⇒y^3=36^3

⇒y=36

Put the value of y in equation (1), and we get

x=324/36

x=9

Hence, this is the answer.

thanks

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