Question

if x =7+4√3 find the value of x power2 +1/x power 2

Answer 1

$\textbf{Answer :}$

Given that,

x = 7 + 4√3

So, 1/x = 1/(7 + 4√3)

We rationalize the denominator by multiplying both the numerator and the denominator by (7 - 4√3)

= (7 - 4√3)/{(7 + 4√3)(7 - 4√3)}

= (7 - 4√3)/(49 - 28√3 + 28√3 - 48)

= (7 - 4√3)/1

= 7 - 4√3

So, x + 1/x

= 7 + 4√3 + 7 - 4√3

= 14

∴ x² + 1/x²

= (x + 1/x)² - (2 * x * 1/x)

= 14² - 2

= 196 - 2

= 194

#$\textbf{MarkAsBrainliest}$

Answer 2

Heya!!

★Answer★

Given,

x=7+4√3

Now,

1/x

={1 / 7+4√3}

={1 × (7-4√3) / (7+4√3) (7-4√3)}

={ (7-4√3) / (7)^2-(4√3)^2 }

={ (7 - 4√3) / (49) - (16×3)}

={ (7-4√3) / (49-48) }

= { (7-4√3) / 1 }

= (7-4√3)

So,

(x+1/x)

=7+4√3+7-4√3 [Cause ,1/x=(7-4√3)]

=14

Now,

(x)^2 +(1/x)^2

=(x+1/x)^2 - 2 × x × 1/x

=(14)^2 - 2 × {(7+4√3)(7-4√3)}

=196 - 2 {(7)^2-(4√3)^2}

=196 - 2 {(49) - (16×3)}

=196 - 2 × 1

=194

So, x+1/x=194

$hope \: my \: answer \: helped$

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