Question

if x=(7+4√3), then the value of x^2+1/x^2 is

Answer 1

Answer:

the  answer is 194

Step-by-step explanation:

Answer 2

Hi ☺ !!


Here is your answer :


Given : X = ( 7 + 4√3 )


Therefore,

1/X = 1 / 7 + 4√3


1/ X = 1/ 7 + 4√3 × ( 7 - 4√3 ) / ( 7 - 4√3 )


1/ X = ( 7 - 4√3 ) / ( 7 + 4√3 ) ( 7 - 4√3 )


1 / X = ( 7 - 4√3 ) / ( 7)² - ( 4√3)² [ Since ( a + b ) ( a - b ) = a² - b² ]


1 / X = ( 7 - 4√3 ) / 49 - 48

1 / X = ( 7 - 4√3 ) / 1


1 / X = 7 - 4√3.


Therefore,


x + 1 / x = 7 + 4√3 + 7 - 4√3


x + 1 / x = 14.



On squaring both sides , we get

( x + 1/x)² = 14²


x² + 1/x² + 2 x × 1/x = 196


x² + 1/x² + 2 = 196

x² + 1/x² = 196 - 2

x² + 1/x² = 194.


Hence,

x² + 1/x² = 194.



☺ Hope it will help you ☺

$<marquee>$By Rishi403

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