Question

If x=3 + 2√2 find the value of x²+ 1 /x² ans me fast ​

Answer 1

Solution

Given :-

• x = 3 + 2√2 __________(1)

Find :-

• Value of x² + 1/x².

Explantion

First Calculate, 1/x.

==> 1/x = 1/(3 + 2√2)

Rationalize Denominator of R.H.S.

==> 1/x = (3 - 2√2)/(3 + 2√2)(3 - 2√2)

Using Formula

$\boxed{\underline{\tt{\red{\:(a+b)(a-b)\:=\:(a^2-b^2)}}}}$

==> 1/x = (3 - 2√2)/[3² - (2√2)²]

==> 1/x = ( 3 - 2√2)/(9 - 8)

==> 1/x = (3 - 2√2)/1

==> 1/x = (3 - 2√2).

Now, Calculate ( x² + 1/x²)

Keep value of x & 1/x.

==> x² + 1/x² = (3 + 2√2)² + ( 3 - 2√2)²

==> x² + 1/x² = [3² + (2√2)² + 2×3×2√2] + [ 3² + (2√2)² - 2×3×2√2]

==> x² + 1/x² = [ 9 + 8 + 12√2] + [ 9 + 8 - 12√2]

==> x² + 1/x² = [ 17 + 12√2 + 17 - 12√2

==> x² + 1/x² = 34

Hence

• Value of ( x² + 1/x²) will be = 34.

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Answer 2

$\huge\boxed{\fcolorbox{white}{cyan}{Answer:⇢}}$

⠀⠀⠀

$\bf \underline{Solution} :-$

⠀⠀⠀

$\bf \underline{Given} :-$

• x = 3 + 2√2 __________(1)

⠀⠀⠀

$\bf \underline{To \: Find} :-$

• Value of x² + 1/x².

⠀⠀⠀

$\bf \underline{Explanation} :-$

⠀⠀⠀

First Calculate,

• 1/x.

• ➜ 1/x = 1/(3 + 2√2)

∴ Rationalize Denominator of ⠀⠀R.H.S.

• ➜ 1/x = (3 - 2√2)/(3 + 2√2)(3 - 2√2)

⠀⠀⠀

∴$\bf \underline{Using \: Formula} :-$

$\boxed{\underline{\tt{\red{\:(a+b)(a-b)\:=\:(a^2-b^2)}}}}$

• ➜ 1/x = (3 - 2√2)/[3² - (2√2)²]

• ➜ 1/x = ( 3 - 2√2)/(9 - 8)

• ➜ 1/x = (3 - 2√2)/1

• ➜ 1/x = (3 - 2√2).

⠀⠀⠀

∴ Now, Calculate ( x² + 1/x²)

∴ Keep value of x & 1/x.

• ➜ x² + 1/x² = (3 + 2√2)² + ( 3 - 2√2)²

• ➜ x² + 1/x² = [3² + (2√2)² + 2×3×2√2] + [ 3² + (2√2)² - 2×3×2√2]

• ➜ x² + 1/x² = [ 9 + 8 + 12√2] + [ 9 + 8 - 12√2]

• ➜ x² + 1/x² = [ 17 + 12√2 + 17 - 12√2

• ➜ x² + 1/x² = 34

⠀⠀⠀

$\bf \underline{Hence}..,$

• Value of ( x² + 1/x²) will be = 34

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