solve the following equation: x^2-6x+[x]+7=0. how to solve this?
Priya , 7 Years ago
Grade 12
Trigonometry> solve the following equation: x^2-6x+[x]+...
3 Answers
Arun
Dear student
We can always write
[X] = X - r
where 0
Then
X^2 - 6X + [X] + 7 = 0
becomes
X^2 - 5X + 7 - r = 0
or, by completing the square:
(X-5/2)^2 + 3/4 - r = 0
If
|X - 5/2| >= 1/2,
then we would have
(X-5/2)^2 >= 1/4
and therefore
r = (X-5/2)^2 + 3/4 >= 1,
which is a contradiction. Therefore, we must have
|X - 5/2|
or 2
Now it's easier. This means [X] = 2, so
X^2 - 6X + 2 + 7 = 0
(X-3)^2 = 0
X = 3.
HOWEVER, X=3 contradicts [X]=2, so in the end, there is no solution.
[X] = X - r
where 0
Then
X^2 - 6X + [X] + 7 = 0
becomes
X^2 - 5X + 7 - r = 0
or, by completing the square:
(X-5/2)^2 + 3/4 - r = 0
If
|X - 5/2| >= 1/2,
then we would have
(X-5/2)^2 >= 1/4
and therefore
r = (X-5/2)^2 + 3/4 >= 1,
which is a contradiction. Therefore, we must have
|X - 5/2|
or 2
Now it's easier. This means [X] = 2, so
X^2 - 6X + 2 + 7 = 0
(X-3)^2 = 0
X = 3.
HOWEVER, X=3 contradicts [X]=2, so in the end, there is no solution.
Regards
Arun (askIITians forum expert)
suvidhi mehta
you can also make th graph and check you will get no solutions
[x] = 6x β x^2 β 7
hope it helps you..........
Soumendu Majumdar
Dear Student,
so {x} 
But for {x} = 0.75 the value of x = 2.5 , which is impossible
So there is no value of x for which this equation is satisfied.
Hope it helps!
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Other Related Questions on trigonometry
In ABC, if cot A+cot B+cot C = cosecA cosecB cosecC, then prove that ABC is right angle triangle.
In ABC, if cot A+cot B+cot C = cosecA cosecB cosecC, then prove that ABC is right angle triangle.
trigonometry
1 Answer Available
Last Activity: 3 Years ago
- Find the general solution of equation tan3β=cot2β
For all angles between -720 and +720
- Find the general solution of equation tan3β=cot2β
For all angles between -720 and +720
trigonometry
1 Answer Available
Last Activity: 3 Years ago
To prove : Cosec(45 degree - A)Cosec(45 degree + A) = 2SecA
To prove : Cosec(45 degree - A)Cosec(45 degree + A) = 2SecA
trigonometry
1 Answer Available
Last Activity: 3 Years ago
Derive a formula for the area of the triangle, given b, A, B, and C. That is, derive the formula: (b^2sinAsinC)/(2sinB)
Derive a formula for the area of the triangle, given b, A, B, and C. That is, derive the formula: (b^2sinAsinC)/(2sinB)
trigonometry
1 Answer Available
Last Activity: 3 Years ago
WHAT IS THE LIMIT WHEN X TOWARDS TO 0 OF sin6x/5x ? limπ₯β0 π ππ6π₯/5π₯
WHAT IS THE LIMIT WHEN X TOWARDS TO 0 OF sin6x/5x ? limπ₯β0 π ππ6π₯/5π₯
trigonometry
1 Answer Available
Last Activity: 3 Years ago