Math, asked by swatishkl986, 7 months ago

if (x+1/x)=5 then find (x²+1/x²) and (x⁴+1/x⁴)​

Answers

Answered by rsagnik437
48

Correct question:-

If (x+1/x)=5,find (x²+1/x²) and (x⁴+1/x⁴)

Given:-

→(x+1/x=5)

To find:-

Value of :-

→(x²+1/x²)

→(x⁴+1/x⁴)

Solution:-

By squaring both the sides in the

eq. (x+1/x)=5,we get:-

 =  >( x +  \frac{1}{x}) ^{2}   = (5) ^{2}

We know that:-

=>(a+b)²=++2ab

 =  >  {x}^{2}  +  \frac{1}{ {x}^{2} }  + 2 \times x \times  \frac{1}{x}  = 25

 =  >  {x}^{2}  +  \frac{1}{ {x}^{2} } + 2  = 25

 =  >  {x}^{2}  +  \frac{1}{ {x}^{2} } = 25 - 2

 =  >  {x}^{2}  +  \frac{1}{ {x}^{2} } = 23

Here,we have got the value of (x²+1/x²)=23

Now,by squaring both the sides

in the equation (+1/)=23,we get:-

 =  > ( {x}^{2}  +  \frac{1}{ {x}^{2} })^{2} = (23) ^{2}

By using the same identity used above we get:-

 =  >  {x}^{4}  +  \frac{1}{ {x}^{4} }  + 2 \times  {x}^{2}  \times  \frac{1}{ {x}^{2} }  = 529

 =  >  {x}^{4}  +  \frac{1}{ {x}^{4} }  + 2 = 529

 =  >  {x}^{4}  +  \frac{1}{ {x}^{4} }  = 529 - 2

 =  >  {x}^{4} +  \frac{1}{ {x}^{4} }   = 527

Thus:-

Value of (+1/) is 23.

→Value of (x⁴+1/x⁴) is 527.

Answered by Anonymous
5

\huge\red{\underline{❥Answer}}

If (x+1/x)=5,find (x²+1/x²) and (x⁴+1/x⁴)

Given:-

(x+1/x=5)

To find:-

Value of :-

(x²+1/x²)

(x⁴+1/x⁴)

\huge\purple{\underline{Solution}}

By squaring both the sides in the

eq. (x+1/x)=5,we get:-

( x + \frac{1}{x}) ^{2} = (5) ^{2}=&gt;(x+x¹)²=(5)²</p><p></p><h3>We know that:-</h3><p>=&gt; (a+b)²=a²+b²+2ab</p><p>=&gt; [tex]{x}^{2} + \frac{1}{ {x}^{2} } + 2 \times x \times \frac{1}{x} = 25=>x

2

+

x

2

1

+2×x×

x

1

=25

= > {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 25=>x

2

+

x

2

1

+2=25

= > {x}^{2} + \frac{1}{ {x}^{2} } = 25 - 2=>x

2

+

x

2

1

=25−2

= > {x}^{2} + \frac{1}{ {x}^{2} } = 23=>x

2

+

x

2

1

=23

Here,we have got the value of (x²+1/x²)=23

Now,by squaring both the sides

in the equation (x²+1/x²)=23,we get:-

= > ( {x}^{2} + \frac{1}{ {x}^{2} })^{2} = (23) ^{2}=>(x

2

+

x

2

1

)

2

=(23)

2

By using the same identity used above we get:-

= > {x}^{4} + \frac{1}{ {x}^{4} } + 2 \times {x}^{2} \times \frac{1}{ {x}^{2} } = 529=>x

4

+

x

4

1

+2×x

2

×

x

2

1

=529

= > {x}^{4} + \frac{1}{ {x}^{4} } + 2 = 529=>x

4

+

x

4

1

+2=529

= > {x}^{4} + \frac{1}{ {x}^{4} } = 529 - 2=>x

4

+

x

4

1

=529−2

= > {x}^{4} + \frac{1}{ {x}^{4} } = 527=>x

4

+

x

4

1

=527

Thus:-

→Value of (x²+1/x²) is 23.

→Value of (x⁴+1/x⁴) is 527.

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