Cheenta
How 9 Cheenta students ranked in top 100 in ISI and CMI Entrances?
Learn More

Number Theory - AMC 10A, 2018 - Problem 10

Try this beautiful problem from AMC 10A, 2018 based on Number theory.

Problem - Number Theory


Let's try this problem number 10 from AMC 10A, 2018 based on Number Theory.

Suppose that the real number $x$ satisfies $\sqrt {49-x^2}$ - $\sqrt {25-x^2}$ = $3$.

What is the value of $\sqrt {49-x^2}$ + $\sqrt {25-x^2}$?

  • 8
  • $\sqrt 33 + 8$
  • 9
  • $2\sqrt10+4$
  • 12

Key Concepts


Number Theory

Real number

Square root

Check the Answer


Answer: 8

AMC 10 A - 2018 - Problem No.10

Mathematics can be fun by Perelman

Try with Hints


As a first hint we can start from here :

In order to get rid of the square roots, we multiply by the conjugate. Its value is the solution.The \(x^2\) terms cancel out.

\((\sqrt {49 - x^2} +\sqrt {25 - x^2}) (\sqrt {49 - x^2}) -(\sqrt {25 - x^2})\)

= 49 -\(x^2 - 25 + x^2\)

=24

Given that \(\sqrt {49 - x^2}) -(\sqrt {25 - x^2})\) = 3

\(\sqrt {49 - x^2} +\sqrt {25 - x^2}\) = \(\frac {24}{3}\)

= 8

Subscribe to Cheenta at Youtube


Knowledge Partner

Cheenta is a knowledge partner of Aditya Birla Education Academy
Cheenta

Cheenta Academy

Aditya Birla Education Academy

Aditya Birla Education Academy

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.
JOIN TRIAL
support@cheenta.com