Please solve Equation Qs
Tue, 2008-03-18 12:59
Q1. How many common solution exists between (a – b)x2 +(b – c)x +(c – a) = 0 and (c – a)x2 +(b – c)x +(a – b) = 0 ?
a. 0
b. 1
c. 2
d. None of these
Q2. How many triples (x, y, z) of positive integers satisfy the following equation
3x + 4y = 5z.
a. 0
b. 1
c. 2
d. None of these
Tue, 2008-03-18 20:28
#2
ans
Q1. How many common solution exists between (a – b)x2 +(b – c)x +(c – a) = 0 and (c – a)x2 +(b – c)x +(a – b) = 0 ?
a. 0
b. 1
c. 2
d. None of these
Here equation (a – b)x2 +(b – c)x +(c – a) = 0 --------(1)
and (c – a)x2 +(b – c)x +(a – b) = 0 ?---------(2)
so equating both
ax^2-bx^2+bx-cx+c-a=cx^2-ax^2+bx-cx+a-b
so 2a(x^2-1)-b(x^2-1)-c(x^2-1)=0
so X^2-1=0
so x=+/- 1
ans=c
Little Star
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n/a
Q2. There exist only one triplet
(2, 2, 2)
answer is b
It can be proved but i guess the logic involved is beyond CAT standard