Difference between revisions of "1991 AHSME Problems/Problem 27"

Revision as of 13:34, 14 December 2016

If $x+\sqrt{x^2-1}+\frac{1}{x-\sqrt{x^2-1}}=20$ then $x^2+\sqrt{x^4-1}+\frac{1}{x^2+\sqrt{x^4-1}}=$

(A) $5.05$ (B) $20$ (C) $51.005$ (D) $61.25$ (E) $400$

Solution by e_power_pi_times_i

Notice that the first equation equates to $\dfrac{x^2 - (x^2 - 1) + 1}{x - \sqrt{x^2 - 1}} = 20$ . Therefore

1991 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 26	Followed by Problem 28
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
All AHSME Problems and Solutions

@@ Line 6: / Line 6: @@
 == Solution ==
-<math>\fbox{C}</math>
+Solution by e_power_pi_times_i
+Notice that the first equation equates to <math>\dfrac{x^2 - (x^2 - 1) + 1}{x - \sqrt{x^2 - 1}} = 20</math>. Therefore
 == See also ==