I was not getting the correct ans. to the following three questions, Please answer them.
1.The no. of solutions of the equation x6- x5+ x4- x3+ x2- x + 3/4 = 0 is ....
The ans. is given as zero...Please explain.
2.The no. of ordered pairs (a,b,c) such that L.C.M (a,b) = 1000, L.C.M (b,c) = 2000, L.C.M (c,a) = 2000 is....
The ans. is given as 70. Please try and explain if u get it.
3.If alpha is a real root of x3+ 2x2 + 10x - 20 = 0, then
a. alpha is rational
b.(alpha)2 is rational
c. alpha is irrational
d. (alpha)2 is irrational
ans. is given as c,d. Please explain me the ans.
I simplified the eqn. as follows:
x6- x5+ x4- x3+ x2- x + 3/4 = 0
x3(x3 - 1) - x2(x3 -1) +x(x3 - 1) + 3/4 = 0
(x3 - 1)(x3 - x2 + x) + 3/4 = 0
x(x3 - 1)(x2 - x + 1)/(x + 1) + 3/4 = 0
x(x6 - 1)/(x + 1) + 3/4 = 0
Taking L.C.M.,
4x7 - x + 3 = 0
But, I am getting that this equation can be zero, and hence has a soln.
I don't know what is wrong with my solution.
nothing's wrong man but you made it too lengthy i could give you a one step solution
Check up yor answer There is a solution in between 0.18898 to -018898 Hence there is only one solution for the given equation