Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

1963 TMTA High School Algebra I Contest Problem 25

Problem

If $\sqrt{5}=2.236,$ the value of $\frac{1+\sqrt{5}}{3-2\sqrt{5}}$ to the nearest hundredth is:

$\text{(A)} \quad -2.25 \quad \text{(B)} \quad -2.35 \quad \text{(C)} \quad -2.15 \quad \text{(D)} \quad -2.20 \quad \text{(E)} \quad -2.50$

Solution

Simplify the expression first: \[\frac{1+\sqrt{5}}{3-2\sqrt{5}} \cdot \frac{3+2\sqrt{5}}{3+2\sqrt{5}}=\frac{3+3\sqrt{5}+2\sqrt{5}+10}{-17}=\frac{-13+5\sqrt{5}}{11}\] Then we can use our approximation $\sqrt{5}=2.236.$ We see that this is closest to $\boxed{\text{(C)} \quad -2.15}.$

See Also

1963 TMTA High School Mathematics Contests (Problems)
Preceded by
Problem 24 		TMTA High School Mathematics Contest Past Problems/Solutions Followed by
Problem 26
Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1963_TMTA_High_School_Algebra_I_Contest_Problem_25&oldid=144625"