Home
Class 12
MATHS
Let [a] denotes the larger integer not e...

Let `[a]` denotes the larger integer not exceeding the real number `a` if `x` and `y` satisfy the equations `y=2[x]+3` and `y=3[x-2]` simultaneously determine `[x+y]`

Text Solution

Verified by Experts

We have `y=2[x]+3=3[x-2]`……i ltbr `implies2[x]+3=3([x]-2)`[from property (i)]
`implies2[x]+3=3[x]-6`
`implies[x]=9`
From Eq. (i) `y=2xx9+3=21`
`:.[x+y]=[x+21]=[x]+21=9+21=30`
hence the value of `[x+y]` is 30.
Promotional Banner

Similar Questions

Explore conceptually related problems

If x and y satisfy the equations max(|x+y|,|x-y|)=1 and |y|=x-[x] , the number of ordered pairs (x, y).

The number of integral pairs (x, y) satisfying the equation 2x^(2)-3xy-2y^(2)=7 is :

The number of pairs (x,y) which will satisfy the equation x^2-x y+y^2=4(x+y-4) is

Find all the pairs of x,y that satisfy the equation cosx+cosy+cos(x+y)=-3/2

The negation of the statement ''for all real numbers x and y, x+y=y+x'' is

If x and y are real numbers such that x gt y and |x| gt |y| , then :

If 2x-3y=7" and "(a+b)x-(a+b-3)y=4a+b represent coincident lines, then a and b satisfy the equation :

For any real number of x and y, cos x = cos y ,prove that x=2npi+-y where n in Z

Find all number of pairs x,y that satisfy the equation tan^(4) x + tan^(4)y+2 cot^(2)x * cot^(2) y=3+ sin^(2)(x+y) .

Find the values of x, y, z if the matrix A=[(0, 2y,z),(x,y,-z),(x,-y,z)] satisfy the equation A'A=I .