Question

please help me solve this

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Answer 1

Answer:

–√+43–√ ( if so , then already answer is given)

So,

x=(√7+43–√)

Now

7+4(√3)=22+2∗2∗3–√+(3–√)2

=(2+3–√)2

Hence 7+43–√−−−−−−−√ = 2 +3–√

So x=2+(√3)

1/x=1(2+3–√)

=2−3–√22−3–√2 [ multiplying numerator and denominator by 2+(√3) ]

=2−3–√4–3

=2+3–√

So 1/x=2−3–√

So x+1x=(2+3–√)+(2−3–√)=4

If x=7+4√3, then what will be the value of √x+1/√x?

If x=7-4√3, what does x+1/x equal?

If x=3-2√2, then what is the value of (√x) - (1/√x)?

If x=√7+4√3, what is the value of x+1/x=?

What is the value of x+1/x if x=7-4√3?

Given :

x=7–√+43–√

⟹1x=17–√+43–√

⟹1x=1(7–√+43–√)(7–√−43–√)(7–√−43–√)

(a+b)(a−b)=a2−b2

Therefore,

⟹1x=7–√−43–√(7–√)2−(43–√)2

⟹1x=7–√−43–√−41

⟹x+1x=7–√+43–√−7–√−43–√41

⟹x+1x=417–√+1643–√−7–√+43–√41

[math]\implies x + \dfrac{1}{x} = 8\dfrac{5\sqrt{7} + 21\sqrt{[/math]

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x=7+43–√−−−−−−−√x=(2)2+2(3–√)(2)+(3–√)2−−−−−−−−−−−−−−−−−−−√x=(2+3–√)2−−−−−−−−√x=2+3–√(x+1x)=2+3–√+12+3–√⋅2−3–√2−3–√(x+1x)=2+3–√+2−3–√4−3(x+1x)=4

x = √7 + 4√3

1/x = 1/(√7 + 4√3)

1/x = (√7 - 4√3) / (√7 + 4√3) (√7 - 4√3)

1/x = (√7 - 4√3)/ ((√7)^2 - (4√3)^2)

1/x = (√7 - 4√3) / (7 -48)

1/x = -((√7 - 4√3)/41)

x + 1/x = (√7 + 4√3) + (-(√7 - 4√3)/41)

= (√7 + 4√3) - (√7 - 4√3)/41

= (41(√7 + 4√3) - (√7 - 4√3))/41

= {41√7 - √7 + 164√3 + 4√3}/41

= (40√7 + 168√3)/41

If a=√ (7+4√3), what will be the value of a+1÷a?

If x=3+2√2, then what is the value of √x-1/√x?

If ‘x=3-2√2’, can you find the value of ‘√x+1/√x’?

If x=√7+4√3, what is the value of x+1÷x?

If x=3+2√3, then what is the value of √x+1/√x?

Given x =√7+4√3

1/x = 1/(√7+4√3) = (4√3-√7)/(√7+4√3) (4√3-√7) , multiplying numerator and denominator by (4√3-√7)

1/x = (4√3-√7)/41

x+1/x = (√7+4√3) + (4√3-√7)/41

On simplification (56+8√21)/(√7+4√3).

Based on the problem given this should be the answer.

However the first part of x generally given as an integer, and the answer is simple.

Like if 7 is given in place of √7 then the answer would be 14.

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Given, x = (√7 + 4√3)

Now, (√7 + 4√3)*(√7 - 4√3) = 7 - 48 = - 41.

So, x*(√7 - 4√3) = - 41

So, 1 / x = {(√7 - 4√3) / (- 41)}

Therefore, x + 1 / x = (√7 + 4√3) - {(√7 - 4√3) / 41} = {40*(√7) + 42*(4√3)} / 41

question :

solution: (x+1/x) (x+1/x) can also be written as

(x+1/x) (x+1/x) = 1+(1/x) (1/x)

root(7) root(7) = 2.6457513110645907

root(3 root(3 )= 1.7320508075688772

x= 2.6457513110645907 + (4 x 1.7320508075688772)

x= 9.57395454134

now 1/x 1/x = 0.10445004681

(x+1/x) (x+1/x) = 0.10445004681 + 1

therefore (x+1/x) (x+1/x) =1.10445004681

x+1/x can be written as 1+1/x

Now as x=√7+4√3

1/x=1/√7+4√3

on multipling and dividing with

4√3-√7 we get 4√3-√7/(4√3)^2-(√7)^2

=4√3-√7/48–7

4√3-√7/41=1/x

1+1/x=1+4√3-√7/41

I think the answer may not match as in question it should be 7+4√3=x which will give answer as 8–4√3

x= sqrt 7+4sqrt 3 ….,,… (1)

So 1/x=1/{sqrt 7+4sqrt 3}

Or 1/x={sqrt 7–4sqrt 3}/{sqrt 7+4sqrt 3}{sqrt 7–4sqrt 3}

Or 1/x={sqrt 7–4sqrt 3}/{ 7–16* 3}

Or 1/x={sqrt 7–4sqrt 3}/-41

Or 1/x=(4/41)sqrt 3-(1/41) sqrt7 ……(2)

So x+1/x =(4+4/41)sqrt 3 +(1–1/41)sqrt 7

Or x+1/x=(168/41)sqrt 4+(40/41)sqrt 7

If x=√(7+4√3)=(2+√3)

Then 1/x= (2-√3)

Therefore (x+1/x)=4

Given , x=√7+4√3

Now, 1/x= 1/(√7+4√3)

After rationalisation,we get,

1/x=1/(√7+4√3) *(√7–4√3)/(√7–4√3)

1/x= (√7–4√3)/(-41) = (4√3-√7 )/41

Now,

x+1/x= (√7+4√3) +((4√3-√7)/41)

x+1/x= (40√7+168√3)/41….ANS..

A2A!

x = 7 + 4√3

So, 1/x = 7 - 4√3

x + 1/x = 7 + 4√3 + 7 - 4√3 = 14

Hope that helps! !

——AA

x=7^1/2+4.3^1/2………………….(1)

1 /x= 1/( 7^1/2+4.3^1/2) , multiply above and below by (7^1/2 -4.3^1/2).

1/x= (7^1/2 - 4.3^1/2)/(-41)

1/x= -(7^1/2)/41 +(4.3^1/2)/41…………(2)

By adding eq.(1)& eq.(2)

x+1/x= (7^1/2).40/41 +(4.3^1/2).42/41 , answer

Consider, a = 7 – 4√3

= 7 – 2×2×√3

= 4 + 3 – 2×2× √3

= 2

2

+ (√3)

2

– 2×2× √3

a = (2 – √3)

2

∴ √a = 2 – √3

Hence [(√a)+ (1/√a)] = 2 – √3 +2 + √3

= 4

As, x=√7+4√3

So,

X+1/x=

(√7+4√3)+1/ (√7+4√3)

= (√7+4√3)+1/ (√7+4√3)* (√7+4√3)/ (√7+4√3)

=[(-40)/√7+4√3]

Rt(7+4rt3) =rt (7+2rt12)=rt(4+3 +2rt4*3)

(2+rt3)^2

x =(2+rt3)

x +1/x =2+rt3 +1/(2+rt3)

2+rt3+(2-rt3)/(2+rt3)(2-rt3)

2+rt3+(2-rt3)/4–3

= 2+rt3+2-rt3= 4

X=√7+4√3

1/X=√7–4√3. ( By rationalisation)

√7+4√3+√7–4√3

2√7

After rationalising 1/x gets converted into. (4√3-√7)/41

Thus √7+4√3+(4√3-√7)/41 = (40√7+168√3)/41

55+8 root21

_____________

root7+4root3

Simply write reciprocal of x and rationalise and add,you will get the answer.

[x+1 ÷ x]= (x÷x) + (1÷x) = 1 ÷ (√7+4√3)= 1÷ 9.57 = 0.104

Rationalise 1/X and then add

Answer should be 2√7