Join WhatsApp Icon IPMAT WhatsApp Group
Question 26

The number of integer solutions $$(x, y)$$ of the inequality $$x^2 + y^2 \leq 10$$ is

Solution

Share

For each integer $$x$$ with $$x^2 \leq 10$$ (i.e., $$|x| \leq 3$$), count $$y$$ with $$y^2 \leq 10 - x^2$$:

  • $$x = 0$$: $$y^2 \leq 10$$, $$y \in [-3, 3]$$ → 7 values.
  • $$x = \pm 1$$: $$y^2 \leq 9$$, 7 each → 14.
  • $$x = \pm 2$$: $$y^2 \leq 6$$, $$y \in [-2, 2]$$ → 5 each → 10.
  • $$x = \pm 3$$: $$y^2 \leq 1$$, $$y \in [-1, 1]$$ → 3 each → 6.

Total = $$7 + 14 + 10 + 6 = \mathbf{37}$$.

Get AI Help

Video Solution

video

Create a FREE account and get:

  • Download Maths Shortcuts PDF
  • Get 300+ previous papers with solutions PDF
  • 500+ Online Tests for Free

Over 8000+ registered students have benefitted from Cracku's IPMAT Course

Crack IPMAT 2026 with Cracku

Enroll Now
Ask AI