Difference between revisions of "1958 AHSME Problems/Problem 5"
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Bringing everything to the same denominator and combining like terms, we get | Bringing everything to the same denominator and combining like terms, we get | ||
| − | <math>\frac{4 + 2\sqrt2 + 2 - \sqrt2 - \sqrt2 - 2}{2} \Rightarrow \frac{4}{2} \Rightarrow 2 \Rightarrow A</math> | + | <math>\frac{4 + 2\sqrt2 + 2 - \sqrt2 - \sqrt2 - 2}{2} \Rightarrow \frac{4}{2} \Rightarrow 2 \Rightarrow \boxed{A}</math> |
==See also== | ==See also== | ||
Latest revision as of 00:23, 12 March 2017
Problem
The expression 
equals:
Solution
To make this problem easier to solve, lets get the radicals out of the denominator. For 
, we will multiply the numerator and denominator by 
so,
.
Now, the other fraction we need to get the radical out of the denominator is 
. Here, we will multiply by the conjugate again, 
. So that simplifies to
.
So now our simplified equation is
Bringing everything to the same denominator and combining like terms, we get
See also
| 1958 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 4 |
Followed by Problem 6 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
