find a solution

[khanna_sumit]

xx3 = 3

Here's a problem. Let f(x) = xx3. Obviously, f(1) = 1 and f grows with x without bound. It follows that the equation

xx3 = 3
has a solution greater than 1. Find at least one such solution.....

[khanna_sumit]

x^x^3 = 3

Here's a problem. Let f(x) = x^x^3. Obviously, f(1) = 1 and f grows with x without bound. It follows that the equation

x^x^3 = 3
has a solution greater than 1. Find at least one such solution.....

[Eccentric]

X^3 lnX = ln 3
3lnX + ln(lnX) = ln ln 3
y=lnX

so,
3 Y + ln Y = 0.094047827616699016174334332084494 //my calculator

now I give up... will come back with smthing later.

[khanna_sumit]

Originally Posted by Eccentric

i could not get xx3.. what is this...??

i have made the correction

[ronjan]

X = 1.44221

gives u x^x^3 = 2.99943 .

U can try for more decimal digits .

ranjan

[catasp2005]

hey ranjan hw did u work out the ques... didnt understan any of it....

[catquery]

can anybody solve this problem
if a times the ath term of an AP is equal to b times the bth term, find the (a+b)th term.
(a) 0 (b) a^2 - b^2 (c) a-b (d) 1

Originally Posted by catasp2005

hey ranjan hw did u work out the ques... didnt understan any of it....

[Eccentric]

Originally Posted by catquery

can anybody solve this problem
if a times the ath term of an AP is equal to b times the bth term, find the (a+b)th term.
(a) 0 (b) a^2 - b^2 (c) a-b (d) 1

Lest say a*a = b*b = k,
ath term = k/a,
bth term = k/b,
difference = k(1/b-1/a)
difference of AP = k(1/b-1/a)/(b-a) = -k/ab
a+b the term = bth term + a*difference = k/b - a*(k/ab) = 0.

[catquery]

ur answer is right but i did it in different way

if we take ath term as -1 then a times ath term will be -1*-1=1 similarly
if we take bth term as 1 then b times bth term will be 1*1=1
a times ath term=b times bth term i.e. 1 but
(a+b)th term will be = -1+1 = 0 as a = -1 and b = 1

tell me whether i am right or wrong

one more question
a number 20 is divided into four parts that are in AP such that the product of the first and fourth is to the product of the second and third is 2:3. Find the largest part.
(a) 12 (b) 4 (c) 8 (d) 9

[bruno]

2,4,6,8

answer is 8

Originally Posted by catquery

ur answer is right but i did it in different way

if we take ath term as -1 then a times ath term will be -1*-1=1 similarly
if we take bth term as 1 then b times bth term will be 1*1=1
a times ath term=b times bth term i.e. 1 but
(a+b)th term will be = -1+1 = 0 as a = -1 and b = 1

tell me whether i am right or wrong

one more question
a number 20 is divided into four parts that are in AP such that the product of the first and fourth is to the product of the second and third is 2:3. Find the largest part.
(a) 12 (b) 4 (c) 8 (d) 9