Practice30 Create account

The squares of two consecutive natural numbers add up to 313. Find the larger number.

Competition practiceAlgebra

A13
B12
C14
D15

Step-by-Step Solution

n^{2} + (n + 1)^{2} = 313

gives

2 n^{2} + 2 n - 312 = 0, n^{2} + n - 156 = 0

, so

n = 12

and the larger is 13.

Answer: A) 13

Master this topic in 30 minutes a day.

Don't just memorise the answer — build a daily practice habit.

Practice 5 Similar Questions Free →

All Algebra practice questions

More Algebra practice

For what positive k does x² − 2(k − 1)x + (k + 5) = 0 have equal roots?The roots of ax² + bx + c = 0 are in the ratio 2 : 3. Which relation holds?α and β are the roots of x² − 5x + 3 = 0. Which equation has roots α + 1/β and β + 1/α?x = 2 is a root of x² + ax − 10 = 0, and x² + ax + b = 0 has equal roots. Find b.Find the value of √(12 + √(12 + √(12 + …))) (continuing without end).