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If x=2+√3 then find x cube +1/x cube what is the answer please tell me

Anurag13 aswale, 4 years ago

Grade:9

13 Answers

Anoop

12 Points

4 years ago

x = 2 + ∫3 , 1/x = 2-∫3

So, x + 1/x = 4

(x+1/x)^{3 =} 4³

x³ + 1/x³ + 3x + 1/x = 64

x³ + 1/x³ + 3 = 64

x³ + 1/x^{3 =} 64 – 3 = 61

praneethvikram

46 Points

4 years ago

given x = 2+ sqrt (3) => 1/x will be 2- sqrt(3)

=> x + 1/x = 4

cubing on both sides

=> x^3 + 1/x^3 = 64-3 = 61

Arun

25763 Points

4 years ago

if we find

x+1/x = 4

now (x + 1/x)³ = x³ + 1/x³ + 3* x* 1/x (x + 1/x)

4³ = x³ + 1/x³ + 3* 4

x³ + 1/x³ = 64 –12 = 52

praneethvikram

46 Points

4 years ago

given x = 2+ sqrt (3) => 1/x will be 2- sqrt(3)

=> x + 1/x = 4

cubing on both sides

=> x^3 + 1/x^3 = 64-3(4) = 52

sorry for the mistake done

Kunal friends

13 Points

4 years ago

x=2+∫3 [given]

x+1/x =2+∫3+1/2+∫3

=[2+∫3][2+∫3]+1/2+∫3 [taking LCM ]

=[2+∫3]²+1/2+∫3

=4+3+[4×∫3]+1/2+∫3

=8+4∫3/2+∫3

=[8+4∫3/2+∫3]×[2-∫3/2-∫3] [by rationalising the denominator]

=[8+4∫3][2-∫3]/[2]²-[∫3]²

=16-8∫3+8∫3-4[∫3]²

=16-12

x+1/x=4

[x+1/x]³=4³ [cubing both side]

x³+1/x³+3×x×1/x[x+1/x]=64 [using {x+y}³]

x³+1/x³+3×4=64 [substituting the value of x+1/x]\

x³+1/x³=64-12

x³+1/x³=52 [Ans]

Mohd Mujtaba

131 Points

4 years ago

(x+1/x)^3=x^3+1/x^3+3x+3/x . Given x=2+root3. So put value in above we get answer 52. Hope you understand thank ☺☺☺☺☺

yathartha gupta

71 Points

4 years ago

x=2+∫3 [given]x+1/x =2+∫3+1/2+∫3 =[2+∫3][2+∫3]+1/2+∫3 [taking LCM ] =[2+∫3]2+1/2+∫3 =4+3+[4×∫3]+1/2+∫3 =8+4∫3/2+∫3 =[8+4∫3/2+∫3]×[2-∫3/2-∫3] [by rationalising the denominator] =[8+4∫3][2-∫3]/[2]2-[∫3]2 =16-8∫3+8∫3-4[∫3]2 =16-12x+1/x=4[x+1/x]3=43 [cubing both side]x3+1/x3+3×x×1/x[x+1/x]=64 [using {x+y}3]x3+1/x3+3×4=64 [substituting the value of x+1/x]\x3+1/x3=64-12x3+1/x3=52 [Ans]

C.Vishaal

39 Points

4 years ago

Alright since x = 2 + root 3, upon rationalistaion, we get 1/x as 2 – root 3.

Alright, do { x + 1/x }³ = x³ + 1/x³ + 3 ( x multiplied by 1/x } …......{1}

So that will give you (2 + root 3 + 2 – root 3)³ = 4³ = 64

When 3 in {1} is taken to the other side, its sign will become negative ( Due to transposition )

That x³ + 1/x³ = 64 – 3 = 61

Hope this answer helps you.

11 Points

3 years ago

All the Answers are wrong

x = 2 + √3

1/x = - 2√3

( x – 1/x)^3= -24√3

ediots

so remember my advise use the brains not the mouths

C.Vishaal

39 Points

3 years ago

1/x cannot be -2 + root 3, you have to rationalise the Denominator So your answer which is I guess -24/3 is wrong.

Nikhil Chouti

27 Points

3 years ago

x=2+√3

1/x=1/2+√3 which upon rationalising we get 2-√3

x^3+1/x^3=2+√3 + 2-√3

Therefore 4 is the answer

Nikhil Chouti

27 Points

3 years ago

Oh sorry the answer would be 52 since we r cubing

We should use (a+b)^3 formula n (a-b)^3 formula to get solution

Ajeet Tiwari

askIITians Faculty 86 Points

one year ago

hello students

since x=1/x
if we find
x+1/x = 4
now (x + 1/x)3= x3+ 1/x3+ 3* x* 1/x (x + 1/x)
43=x3+ 1/x3+ 3* 4
so
x3+ 1/x3= 64 –12 = 52

Hope it helps
Thankyou and Regards