Q. If x = 3 + 3^1/2, then what is the value of x^2 + 9/x^2?

• Given x=3+3^1/2 x^2=9+3+2(3)(3^1/2)=12+6(3)^1/2
  1/x=1/(3+3^1/2
  to find x^2 + 9/x^2=12+6(3)^1/2+(((12-6(3)^1/2)/36)*9=15+9/2(3)^1/2
• 11 years agoHelpfull: Yes(14) No(5)
• 1/x => (3-√3)/3,
  x^2 => 12+6√3,
  x^2+9/x^2 => [x^2+(3/x)^2+{2*x+(3/x)}]-{2*x*(3/x)}
  => {(x+3/x)^2-6}
  => {(3+√3)+3*(3-√3)/3}^2-6
  => (3+√3+3-√3)^2-6
  => 36-6 => 30 Ans.
• 11 years agoHelpfull: Yes(5) No(24)
• Isn't correct
  
  x = 3 + 3^(1/2) = 3 + 1.732 = 4.732
  then
  ( (4.732)^4 + 9 ) / (4.732)^2
  results : 22.79375642
• 10 years agoHelpfull: Yes(5) No(2)
• hi krishna pls explain x^2 + 9/x^2=12+6(3)^1/2+(((12-6(3)^1/2)/36)*9=15+9/2(3)^1/2
• 10 years agoHelpfull: Yes(2) No(1)
• (x-3)^2=3
  x-3=root3
  x^2+9-6x=3
  x^4+9x^2=3x^2+6x^3
  (x^4+9x^2)/x^2=3+6x
  (x^2+9/x^2)=3+6(3+root3)=21+6*root3
• 11 years agoHelpfull: Yes(1) No(3)
• first up-whole we find the value of X.
  so, X=3+3^1/2=3+1.3=4.5
  THEN x^2+9/x^2 =4.5^2+9/4.5^2= 20.25+9/20.25
  20.25*20.25+9/20.25=419.0625/20.25= 20.9
  
• 10 years agoHelpfull: Yes(1) No(1)
• 1/x => (3-√3)/3,
  x^2 => 12+6√3,
  x^2+9/x^2 => [x^2+(3/x)^2+{2*x+(3/x)}]-{2*x*(3/x)}
  => {(x+3/x)^2-6}
  => {(3+√3)+3*(3-√3)/3}^2-6
  => (3+√3+3-√3)^2-6
  => 36-6 =>30
• 11 years agoHelpfull: Yes(0) No(3)
• after substituting x value in eqn we get,
  x^2+9/x^2= -((3+3^1/2))/2
  = -x/2
  ans is -x/2.
  
• 11 years agoHelpfull: Yes(0) No(1)
• @DSS SUNEEL , (x^4+9x^2)/x^2 gives (x^2+9) but not (x^2+9/x^2)
• 11 years agoHelpfull: Yes(0) No(0)
• x^2=(3+3^1/2)^2=3^2+3=12
  so 12+9/12=51/4
• 11 years agoHelpfull: Yes(0) No(2)
• x=3+3^1/2 ==>x=3+3/2 ==>x=6/2 ==> x=3
  x^2+9/x^2 ==>3^2+9/3^2 = 9+9/9 = 18/9 =2
• 10 years agoHelpfull: Yes(0) No(2)
• x=3+3^1/2,1/x=3-3^1/2
  so answer is 5.6848
• 10 years agoHelpfull: Yes(0) No(1)