@jain4444 said:Find the number of integer quadruples (a,b,c,d) with 0 ≤ a,b,c,d ≤ 100, such that a and b are the roots of the quadratic equation x^2 − cx + d = 0, while c and d are the roots of the quadratic equation x^2 − ax + b = 0.
101 solns.
@albiesriram said:Before starting to paint, Billu had 130 litres of blue paint, 164 litres of red paint, and 188 litres of white paint. Billu painted four equally sized stripes on a wall, making a blue stripe, a red stripe, a white stripe, and a pink stripe. Pink is a mixture of red and white, not necessarily in equal amounts. When he finished, he had equal amounts of blue, red, and white paint left. Find the total number of litres of paint Billu had left.?
114
@jain4444 said:Find the number of integer quadruples (a,b,c,d) with 0 ≤ a,b,c,d ≤ 100, such that a and b are the roots of the quadratic equation x^2 − cx + d = 0, while c and d are the roots of the quadratic equation x^2 − ax + b = 0.
a+b = c --- (1)
a*b = d --- (2)
c+d = a --- (3)
c*d = b --- (4)
Add (1) and (3)
a+b+c+d = c+a
=> b+d=0
so b=d=0 is the only available choice of numbers here..
Put this in (1), we get
a=c=x (say)
(x,0,x,0) = (0,0,0,0);(1,0,1,0),...,(100,0,100,0)
so 101 solutions ??
@RDN said:@jain4444a+b = cc+d = aadding , b + d = 0, so b=d=0 and a=c therefore 101 solutions
when you consider product of roots.,,
ab = d
cd = b;
Substituting (2) in (1),
cab=b i.e; ca = 1.
Hence, a = c = 1.
In this case we can have only one soln.
a=1
b=0
c=1
d=0.
Not sure if I'm right.. Plz clarify where I went wrong..
@viewpt said:101 solns.
@sbharadwaj in the step cab=b, you are ignoring the condition in which b=0 and ac != 1, so you are missing out on a set of valid solutions
@jain4444 said:Find the number of integer quadruples (a,b,c,d) with 0 ≤ a,b,c,d ≤ 100, such that a and b are the roots of the quadratic equation x^2 − cx + d = 0, while c and d are the roots of the quadratic equation x^2 − ax + b = 0.
101 ?
@RDN said:@sbharadwaj in the step cab=b, you are ignoring the condition in which b=0 and ac != 1, so you are missing out on a set of valid solutions
hmmm..! gotcha.. 
Thanks :)
Thanks :)@sbharadwaj said:when you consider product of roots.,,ab = dcd = b;Substituting (2) in (1),cab=b i.e; ca = 1.Hence, a = c = 1. In this case we can have only one soln. a=1b=0c=1d=0.Not sure if I'm right.. Plz clarify where I went wrong..
just chk @Logrythym bhai has solved
@idontlikecats said:@viewpt how to solve such a question?
like this:
130 - x = 164 - (x+a) = 188-(2x-a)
x= 92
a = 34
34*3 = 114
130 - x = 164 - (x+a) = 188-(2x-a)
x= 92
a = 34
34*3 = 114
@idontlikecats said:92?
92 is the total amount I need to make of pink....to bring the other two colours to the same level as blue...
regards
scrabbler
regards
scrabbler
@ChirpiBird said:total codes = 9*10= 90digits that can cause confusion 0,1,6,8,95C2 = 10ways.and they can be mirrored so .... 10*2 = 20but here 69 when mirrored is 69 only.90-20 +1 = 71 numbers?EDIT : 11, 88 should also be considered just like 69.. total 73?
10 when mirrored becomes 01 which cannot be valid according to the questiion
Q: 37^47^57^101 div by 103 R?
if n is a positive int such that 2n has 28 divisors and 3n has 30 positive divisores,find the number of divisors for 6n...plz give a detailed xplanation ..thanks in advance
Q. a boy n a girl r riding bicycles on the edge of a circular lake .the boy rides at a speed of 5mps n the girl wid a speed of 4mps . if they travel in same direction the boy wld overtake the girl for the second time aftr 14 mins n 40 sec . hw far is the girl frm the starting pt , wen they meet for the third time in case they r travelling in oppo dir ??
soln needed .
@aditi88 said:if n is a positive int such that 2n has 28 divisors and 3n has 30 positive divisores,find the number of divisors for 6n...plz give a detailed xplanation ..thanks in advance
35? if the answer is right i will post the approach
@Abir1103 said:Q. a boy n a girl r riding bicycles on the edge of a circular lake .the boy rides at a speed of 5mps n the girl wid a speed of 4mps . if they travel in same direction the boy wld overtake the girl for the second time aftr 14 mins n 40 sec . hw far is the girl frm the starting pt , wen they meet for the third time in case they r travelling in oppo dir ??soln needed .
i am getting approx 147 miles.. if the answer is correct i will post the approach
@iLoveTorres said:35? if the answer is right i will post the approach
ans s nt given but n is gvn as 2^5*3^3
@iLoveTorres said:10 when mirrored becomes 01 which cannot be valid according to the questiion
.. i didnt count them in total itself...
otherwise total would have been 10*10.
i took 9*10. ...
otherwise total would have been 10*10.
i took 9*10. ...