Question

never ever mane kabhi kisi bhi ladke ko propose nhi kiya but ek bar kiya tha but vo mera dare tha

ab kiski bari hai

adu or sohan on aye kya ​

Answer 1

Ha

⇝ Question :-

If the mean of \large\rm x \: \: and \: \: \dfrac{1}{x}xand

x

1

is M.

And the mean of \large\rm x^2 \: \: and \: \: \dfrac{1}{x^2}x

2

and

x

2

1

is KM²

then Find the Value of K.

⇝ Answer :-

\large\pink{\pmb{\frak{ \text The \: \text Value \: of \: \text K \: is \: 2}}}

TheValueofKis2

TheValueofKis2

⇝ Step by step Explanation :-

❒ Given in the Question that the mean of \large\rm x \: \: and \: \: \dfrac{1}{x}xand

x

1

is M,

\begin{gathered}:\longmapsto \rm \frac{x + \dfrac{1}{x} }{2} = M \\ \end{gathered}

:⟼

2

x+

x

1

=M

\begin{gathered}:\longmapsto \rm x + \frac{1}{x} = 2M \\ \end{gathered}

:⟼x+

x

1

=2M

\large \bigstar★ Squaring Both Sides :

\begin{gathered}:\longmapsto \rm \bigg(x + \frac{1}{x} \bigg)^{2} = 4 {M}^{2} \\ \end{gathered}

:⟼(x+

x

1

)

2

=4M

2

\begin{gathered}:\longmapsto \rm {x}^{2} + \frac{1}{x {}^{2} } + 2.x. \frac{1}{x} = 2M {}^{2} \\ \end{gathered}

:⟼x

2

+

x

2

1

+2.x.

x

1

=2M

2

\begin{gathered}:\longmapsto \rm {x}^{2} + \frac{1}{{x}^{2} } + 2 = 4M {}^{2} \\ \end{gathered}

:⟼x

2

+

x

2

1

+2=4M

2

\begin{gathered}\purple{ :\longmapsto \underline {\boxed{{\bf {x}^{2} + \frac{1}{ {x}^{2} } = 4M {}^{2} - 2} }}} \\ \end{gathered}

:⟼

x

2

+

x

2

1

=4M

2

−2

❒ Also According To Question the mean of \large\rm x^2 \: \: and \: \: \dfrac{1}{x^2}x

2

and

x

2

1

is KM² ,

\begin{gathered}:\longmapsto \rm \frac{ {x}^{2} + \dfrac{1}{ {x}^{2} } }{2} = {KM}^{2} - 1 \\ \end{gathered}

:⟼

2

x

2

+

x

2

1

=KM

2

−1

\begin{gathered}:\longmapsto \rm {x}^{2} + \frac{1}{ {x}^{2} } = 2(KM {}^{2} - 1) \\ \end{gathered}

:⟼x

2

+

x

2

1

=2(KM

2

−1)

\begin{gathered}:\longmapsto \rm {x}^{2} + \frac{1}{ {x}^{2} } = 2KM {}^{2} - 2 \\ \end{gathered}

:⟼x

2

+

x

2

1

=2KM

2

−2

\large \red\bigstar★ Substituting Value of \large\rm x^2 + \dfrac{1}{x^2}x

2

+

x

2

1

:

\begin{gathered}:\longmapsto \rm 4M {}^{2} - \cancel{2}= 2KM {}^{2} - \cancel{2} \\ \end{gathered}

:⟼4M

2

−

2

=2KM

2

−

2

\begin{gathered}:\longmapsto \rm 4 \: \cancel{M {}^{2} } = 2 K \: \cancel{M^{2} } \\ \end{gathered}

:⟼4

M

2

=2K

M

2

\begin{gathered}:\longmapsto \rm2 K =4 \\ \end{gathered}

:⟼2K=4

\begin{gathered}:\longmapsto \rm K = \cancel \frac{4}{2} \\ \end{gathered}

:⟼K=

2

4

\purple{ \large :\longmapsto \underline {\boxed{{\bf K = 2} }}}:⟼

K=2

Therefore,

\large \bf \blue\maltese \: \: \orange{ \underbrace{ \underline{The\:Value \: of \: K \: is \: 2}}}✠

TheValueofKis2