Question

If x= 3-2√2, find the value of x squre+1/x square​

Answer 1

Answer:

5.86

Step-by-step explanation:

given, x= 3 - 2√ 2

then x^2=(3 - 2√2)^2

= 9 + 8 -12√2

=17 - 12√2......(1)

now 1/x = 1/(3 - 2√2)

= 1 *(3+ 2√2) / (3- 2√2) * (3+2√2)

=3 + 2√2/ 9 - 8...(a^2 - b^2 = (a + b) * (a - b)

=3+2√2...(2)

now add (1)..+ (2)

x^2 + 1/x = 17- 12√2 + 3+2√2

= 20 - 10√2

= 20 - 14.14 (√2=1.414)

=5.86..ans

Answer 2

Answer:

Given:

x=3-2$\sqrt{2}$

$x^{2}$ = $(3-2\sqrt{2} )^{2}$

$x^{2}$ = $9-4\sqrt{2} +8$

$x^{2}$ = $17-4\sqrt{2}$               ⇒ 1

$1/x^{2}$ = $1/17-4\sqrt{2}$        ⇒From 1

Thus,

$x^{2} +1/x^{2} =17-4\sqrt{2} + 1/17-4\sqrt{2}$

$x^{2} +1/x^{2} = (17-4\sqrt{2})^{2}/17-4\sqrt{2} + 1/17-4\sqrt{2}\\x^{2} +1/x^{2} = 289 - 8\sqrt{2} + 32/17-4\sqrt{2} + 1/17-4\sqrt{2}\\ x^{2} +1/x^{2} = 320 -12\sqrt{2}/17-4\sqrt{2} \\x^{2} +1/x^{2} = 320-12\sqrt{2}(17+4\sqrt{2} ) / 289-32\\x^{2} +1/x^{2} = 5440+1280\sqrt{2} - 204\sqrt{2} - 96 /257\\x^{2} +1/x^{2} = 5344 +1076\sqrt{2}/257\\x^{2} +1/x^{2} = 5344+1076(1.41)/257\\x^{2} +1/x^{2} = 5344+1517.16/257\\x^{2} +1/x^{2} = 6861.16/257\\x^{2} +1/x^{2} = 26.697\\x^{2} +1/x^{2} = 26.70$