Question

if (X+1/X)= 4 , find the value of (x²+2/x²).​

Answer 1

Answer:

$\huge\bf\underline\red{AnSweR:}$

$x + \frac{1}{x} = 4$

${(x + \frac{1}{x} }) ^{2} = 16$

${x}^{2} + \frac{1}{ {x}^{2} } + 2 = 16$

${x}^{2} + \frac{1}{ {x}^{2} } = 16 - 2$

$\implies\bf\purple{14}$

Answer 2

Step-by-step explanation:

x=2+√3

1/x=1/2+√3

=1×(2-√3)/(2+√3)(2-√3)

=(2-√3)/ (2^2-√3^2)

=(2-√3)/4-3

=(2-√3)

Therefore

x^2 =(2+√3)

=(2)^2+(√3)^2+2×2×√3

= 4+3+4√3

=7+4√3

1/x^2=(2-√3)^2

(2)^+(√3)^2-2×2×√3

=4+3-4√3

=7-4√3

x^2+1/x^2

=(7+4√3)+(7-4√3)

=7+7+4√3-4√3

=14

hope it helps you