Good algebra problem explanation required
1. If b,c and d are constants and x^2+bx+c=(x+d)^2 for all values of x, what is the value of c?
2. If a,b,k and m are positive integers, is a^k a factor of b^m?
1) a is a factor of b
3. Is Mod x-y>Mod x-z?
1) Mod x > Mod z
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I got the below answers for the questions
Explanations are pretty hard to explain here..but I will try
1. if you expand the first question, you will get the below eqn
If you match this eqn, you will get, b=2d; and c=d^2 or c=b^2/4
either of the answer choices would help to get the value of C, so D
2. b^m/a^k = integer;
1. a is a factor of b
b/a= integer; lets say b=10; a =2
then the main eqn, 10^m/2^k
lets say m=5, k=1; then 10^5/2^1 is an integer
try other values you will get the same so A/D
lets say k=m=2; this wont help, as the values of b and a can be any and b/a can be integer or not. so B wrond.
lets say x=-5, z=-3, this satisfies the above eqn. Substituet this in main eqn, then we get, |5+y|>2; here y can be any value, and may or might not satisfy the equation. So A is wrong
2. x<0; y , z can have any value so B wrong.
3. the values we have chose for x in choice 1, x=-5 and z=-3 didnt satisfy hence E
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Agree with Vigngmat on the answers for Q1 and Q3.
Regarding the Q2,
1. a is a factor of b.
Going by your approach, let a=2, b=10. Now if I reverse the values that you gave for k and m, so that k=5, m=1. Now here, 2^5 is not a factor of 10^1. So I cannot deduce that a^k is a factor of b^m just from the 1st statement given. So statement1 is NOT SUFFICIENT. So the answer cant be A.
Unless we know about a and b, we cannot deduce anything about a^k being a factor of b^m. So NOT SUFFICIENT.
Lets take 1 and 2 together, if a is a factor of b and k=m, then
a^k = a*a*a*....k times. -----------eq1
b^m = b*b*b*....k times (since k=m)----------eq2
now if a is a factor of b, then b/a = a positive integer, say X
divide eq2 by eq1 and we get
(b*b*b....k times)/(a*a*a....k times) = (b/a)^k = X^k
So, we deduce that a^k is a factor of b^m. So (1) and (2) taken together are SUFFICIENT.
So C should be the answer.
Originally Posted by vigngmat
1 D as bx+c=2dx+d^2, so from 1 we know d and so know c as c=d^2, from 2 we know d, from d we know c.
2 C agree with callmedaone
3 E no info about y given
I think the answer of
x^2+bx+c=(x+d)^2 for all values of x
so if the equations is correct for all values of X we can input X =0
A says D=3
Agree with answers for 2 and 3.
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hey guys could you explain the first one in little details..
my method seem little specious although ans i have got is D only ...
thanks in advance ...
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