Question

If x = 3-2 √2 then find the value of (x ^ 2 - 1/ x^ 2).

Answer 1

If x=3-2√2;

then the value of (x^2--1/x^2) is

={(3--2√2)^×2--1/(3--2√2)^×2}

={(9+8)×2--1/2}

={34--1/2}

=67/2

=33.5

hope it helps you............................

thanks_______$_

Answer 2

$\huge\bold{Answer}$

$\underline\bold{Given}$ => 3 - 2√2.

$\underline\bold{To \:Find}$=> ${x}^{2}$

$\boxed{\textbf{Rationalizing the denominator}}$

= >( 1/ 3 - 2√2) × (3 + 2 √2 / 3 - 2√2)..3 + 2 √2 /${3}^{2}$ - ${(2 √2 )^{2}$

= > 3 + 2√2 /9 -8

= >3 + 2√ 2

= >${x}^{2}$ - 1/ ${x}^{2}$

= >(3-2√2)^2 - (3+2√2)^2

= >${3}^{2}$ - (2√2)^2 + 2 × 3 × 2√2 -

= >[3^2 + (2√2)^2 + 2 × 3 × 2√2]

= >9 - 8 + 12 √2 - ( 9 + 8 +12 + √2)

= >9 - 8 +12 √2 - 9 - 8 - 12 √2.

= >- 16.