Question

x = (√3 + √2) / (√3 - √2) , then find the value of (x + 1/x)².​

Answer 1

Step-by-step explanation:

x = (√3 + √2) / (√3 - √2)

=(√3+√2)/(√3-√2)×(√3+√2)/(√3+√2)

=(√3+√2)²/(√3)²-(√2)²

=(√3)²+(√2)²+2√3√2/3-2

=3+2+2√6

x=5+2√6

(x+1/x)²

=x²+1/x²+2×x×1/x

=x²+1/x²+2

=(5+2√6)²+ [1/(5+2√6)]²+2

=25+24+20√6+[1/25+24+20√6]+2

=49+20√6(49+20√6)+1+2(49+20√6)

=2401+2400+1960√6+1+98+40√6

=4900+2000√6

Answer 2

Answer:

Given,

x = ( √3 + √2) / ( √3 - √2)

Therefore,

( x + 1/ x) ^2

=> x2 + 1 + 1/ x2

=> (√3 + √2)^2 / ( √3 - √2)^2 + 1 + 1 / (√3 + √2)^2 / ( √3 - √2)^2. [ From given]

=> (3 + √6 + 2 / 3 - √6 + 2) + 1 + 1 / ( 3 + √6 + 2 / 3 - √6 + 2)

=> ( 5 + √6 / 5 - √6) + 1 + ( 5 - √6 / 5 + √6)

=> ( 5 + √6) ^2 + [ ( 5+ √6) (5- √6)] + (5- √6)^2 / [ ( 5+ √6) (5+ √6) ]

=> 25 + 5√6 + 6 + 25 + 5√6 - 5√6 -6 + 25 - 5√6 + 6 / 25 + 5√6 - 5√6 - 6

=> 25 + 6 + 25 - 6 +5√6 - 5√6 + 25 + 6 / 25 - 6

=> 25+ 25 + 6 +6 +19 / 19

=> 50 + 12 + 19 / 19

=> 62 + 19 / 19

=> 81 / 19