1979 AMC 12 Problem 7

Attempt Problem 7 of the 1979 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1979 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

The square of an integer is called a perfect square. If

x

is a perfect square, the next larger perfect square is

x+1

x^2+1

x^2+2x+1

x^2+x

x+2\sqrt x+1

Write

x=n^2

for a nonnegative integer

n

Expand the next square

(n+1)^2

and replace

n

\sqrt x

Let

x=n^2

with

n\ge0.

The next larger perfect square is

\begin{aligned} (n+1)^2&=n^2+2n+1\\ &=x+2\sqrt x+1. \end{aligned}

Therefore, the correct answer is E.

Problem 7 in other years