Question

If x = 3 + 31/2, then what is the value of x2 + 9/x2 ?

Answer 1

The value of x² + 9/x²  = 342.28

Given:

x = 3 + 31/2

To find:

The value of x² + 9/x²

Solution:

Given x = 3 + 31/2

⇒ x = 37/2    [ 2 × 3 + 31 = 7 ]

Given problem  x² + 9/x²  

Substitute x = 37/2 in given problem

⇒ $(\frac{37}{2} )^{2} + \frac{9}{(\frac{37}{2} )^{2} }$

⇒ $(\frac{37}{2} )^{2} + \frac{9(2)^{2} }{{37}^{2} }$

⇒ $\frac{1369}{4} + \frac{36 }{{1369} }$

⇒ $\frac{(1369)(1369)+ 4(36) }{{(4)1369} }$

⇒ 342.28

The value of x² + 9/x²  = 342.28

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Answer 2

Answer:

The answer to the given question is

${x}^{2} + \frac{9}{ {x}^{2} } = 342.28$

Step-by-step explanation:

Given :

$x = 3 + \frac{31}{2}$

To find :

we have to find the value of

${x}^{2} + \frac{9}{ {x}^{2} }$

Solution:

The value of x is given as

$x = 3 + \frac{31}{2}$

on adding we get the value of x as

$x = \frac{6 + 31}{2} \\ = \frac{37}{2}$

we have to find the value of

${x}^{2} + \frac{9}{ { x }^{2} }$

On substituting the value of x in the above expression, we have the expression as

${( \frac{37}{2}) }^{2} + \frac{9}{ {( \frac{37}{2} )}^{2} }$

we have to solve the above expression to find the value of x.

${( \frac{37}{2} )}^{2} + \frac{(9)( {2}^{2} )}{ {(37)}^{2} }$

on expanding the values will be

$\frac{1369}{4} + \frac{36}{1369}$

By taking the LCM and adding the values we get the answers as

$\frac{(1369)(1369) + 4(36)}{(4)(1369)}$

on further dividing, we get the value as

$342.28$

Therefore, the final answer to the given question is obtained as the value of

${x}^{2} + \frac{9}{ {x}^{2} } = 342.28$

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