Question

If x = X1 and y = y1 satisfy both the equations y = 2[x] + 3 and y = 3[x – 2] + 5, then
the value of [x1 + yıl is equal to (where [.] represents the greatest integer function)​

Answer 1

given info : x = x₁ and y = y₁ satisfy both the equations y = 2[x] + 3 and y = 3[x - 2] + 5.

To find : the value of |x₁ + y₁| is equal to

solution : here y = 2[x] + 3 and y = 3[x - 2] + 5

We know, [x ± k] = [x] ± k, for any integer k

So, [x - 2] = [x] - 2 , as 2 is an integer number

So, y = 3[x - 2] + 5 = 3[x] - 6 + 5 = 3[x] -1

Let's equate both equation.

2[x] + 3 = 3[x] - 1

⇒3 + 1 = 3[x] - 2[x]

⇒4 = [x]

Integral value of x = x₁ = 4

so, y= 2[x] + 3 = 2 × 4 + 3 = 11 = y₁

so the value of |x₁ + y₁| = 4 + 11 = 15