Question

Find all ordered pair of numbers (x,y) for which it holds
sin (x^2-5y)- 1 is greater than equal to x^4/2020

Answer 1

Given :  sin (x²-5y)- 1 is greater than equal to x⁴/2020

To Find : all ordered pair of numbers (x,y) for which it holds true

Solution:

sin (x²-5y)- 1

-1  ≤ sin α ≤ 1

=> - 1  ≤ sin (x²-5y) ≤ 1

Subtracting 1 each side

=> - 1 - 1  ≤ sin (x²-5y) - 1 ≤ 1 - 1

=> - 2   ≤ sin (x²-5y) ≤ 0

sin (x²-5y) ≤ 0

x⁴/2020  ≥ 0

Hence only possible case is

when  sin (x²-5y)  =  x⁴/2020  = 0

x⁴/2020 = 0 when x = 0

  sin (x²-5y) = 0

=>  sin (-5y) = 0

=> - sin (5y) = 0

=> sin (5y) = 0

 5y  = nπ

=>  y =   nπ/5   where  n  ∈ Z

All ordered pairs  ( 0 ,    nπ/5 )

Learn More:

How many ordered pairs of (m,n) integers satisfy m/12=12/m ...

brainly.in/question/13213839

Identify the ordered pairs that result in a quadrilaterala) (1.-1), (2,-2 ...

brainly.in/question/17225822