Let x-=sqrt(4+sqrt(4+sqrt(4+...to infinity.Then x equals
(a) 3
(b) (sqrt(13)-1)/2
(c) (sqrt(13)+1)/2
(d) sqrt(13)
2006-08-14 17:47:02 · 6 answers · asked by Rohit C 3 in Science & Mathematics ➔ Mathematics
Let x = sqrt(4+sqrt(4+sqrt(4+..
then x^2 = 4 + sqrt(4+sqrt(4+sqrt(4+..
x^2 - x = 4
x^2 - x - 4 = 0
Then x could be [1 + sqrt(17) ] / 2 or [1 - sqrt(17)] / 2
but x cannot be negative so the answer is only
[1 + sqrt(17)] / 2
2006-08-18 04:10:28 · answer #1 · answered by Joe Mkt 3 · 2⤊ 0⤋
Let x-=sqrt(4+sqrt(4+sqrt(4+...to infinity.Then
x= sqrt(4+x)
or x^2 = 4 +x
or x^2 -x -4 +0
by soving the equation
x={1 +squrt(1+16)}/2 and {1 -squrt(1+16)}/2
2006-08-14 18:19:40 · answer #2 · answered by Amar Soni 7 · 0⤊ 1⤋
x = sqrt(4+sqrt(4+sqrt(4 +..)))
x ^ 2 = 4 + sqrt(4+sqrt(4 + sqrt(4 + ...)))
x ^ 2 = 4 + x
x^2 -x -4 = 0
=(-(-1)+sqrt((-1)^2 - 4(1)(-4)))/2(1)
= (1 + sqrt(1 + 16))/2
=2.56
=(-(-1)-sqrt((-1)^2 - 4(1)(-4)))/2(1)
= (1 - sqrt(1 + 16))/2
=-1.56
Answer: 2.56 and -1.56 (None of the above)
2006-08-14 18:32:45 · answer #3 · answered by Taki 2 · 0⤊ 1⤋
follows that x^2=4+x, or x^2-x-4=0, so that x=(1+/- sqrt(17))/2. hence none of a)-d) are correct!
2006-08-14 18:23:43 · answer #4 · answered by whittle 2 · 0⤊ 1⤋
assuming your expression is ?(4 + (?4 - (?4 + (?(4-x))))) ?(4 + (2 - (2 + ?(4-x)))) ?(4 + (2 - 2 + ?(4-x))) ?(4 + ?(4-x)) ?(4) + ^4?(4-x) 2 + ^4?(4-x) can not simplify extra assuming expression is ?(4 + (?4 - (?4 + (?4 - x)))) ?(4 + (?4 - (2 + 2 - x))) ?(4 + (?4 - (4 - x))) ?(4 + (2 - 4 + x)) ?(4 - 2 + x) ?(x+2) can not simplify extra
2016-12-14 06:00:23 · answer #5 · answered by ? 3 · 0⤊ 0⤋
I farted.
2006-08-14 17:53:54 · answer #6 · answered by Anonymous · 0⤊ 3⤋