Math, asked by rajenderpanchagiri, 7 months ago

if x = 2+√3 then the value of x+1/x

Answers

Answered by Anonymous

$\huge\underline\mathfrak{\red{✨ANSWER✨}}$

Let k = x^1/2 +1/x^1/2.

k^2 = x + 1/ x + 2 = (3+2.3^1/2) + 1/(3+2.3^1/2) + 2.

k^2 = ( 5 +2.3^1/2) +1 × (3–2.3^1/2)/(3+ 2.3^1/2)×(3–2.3^1/2).

k^2 =5 + 2.3^1/2 +(3–2.3^1/2)/(9–12).

k^2 = 5 +2.3^1/2- (3- 2.3^1/2)/3.

k^2 =(15+6.3^1/2 -3+2.3^1/2)/3.

k^2 =(12+8.3^1/2)/3 = 4 (3+2.3^1/2)/3.

k = +/- 2{(3+2.3^1/2)/3}^1/2. .put k = x^1/2+ 1/ x^1/2.

x^1/2 + 1/x^1/2 = +/-2{(3+2.3^1/2)/3}^1/2. Answer.

k^2 =5 +2.3^1/2 -1 +(2/3).3^1/2.

k^2 = 4 + (8/3).3^1/2,

k^2 =

Answered by Anonymous

Let k = x^1/2 +1/x^1/2.

k^2 = x + 1/ x + 2 = (3+2.3^1/2) + 1/(3+2.3^1/2) + 2.

k^2 = ( 5 +2.3^1/2) +1 × (3–2.3^1/2)/(3+ 2.3^1/2)×(3–2.3^1/2).

k^2 =5 + 2.3^1/2 +(3–2.3^1/2)/(9–12).

k^2 = 5 +2.3^1/2- (3- 2.3^1/2)/3.

k^2 =(15+6.3^1/2 -3+2.3^1/2)/3.

k^2 =(12+8.3^1/2)/3 = 4 (3+2.3^1/2)/3.

k = +/- 2{(3+2.3^1/2)/3}^1/2. .put k = x^1/2+ 1/ x^1/2.

x^1/2 + 1/x^1/2 = +/-2{(3+2.3^1/2)/3}^1/2. Answer.

.

k^2 =5 +2.3^1/2 -1 +(2/3).3^1/2.

k^2 = 4 + (8/3).3^1/2,

k^2 =

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