text:
## Boxman61 Group Title Solve: ___ ______ √x-2 -1 = √2(x-3) 2 years ago 2 years ago

1. MCronin Group Title

square both sides to get (x-2)-2$\sqrt{x-2}$+1=2x-6 x-1-2$\sqrt{x-2}/]=2x-6 2\[\sqrt{x-2}$=-x+5 $\sqrt{x-2}$=-x+5/2 square both sides again to get x-2=(-x+5/2)^2 x=(-x+5/2)^2+2 x=(x^2-10x+25)/4 +2 4x=x^2-10x+27 x^2-14x+27=0 quadratic from there

2. Boxman61 Group Title

$\sqrt{x-2} -1 = \sqrt{2(x-3)}$ $(\sqrt{x-2})^{2} - (1)^{2} = \sqrt{2x-6}$ $x-2-1 = 2x-6$ $x-3 = 2x-6$ $-x = -3$ x=3

3. MCronin Group Title

no you have o square te entire leftside so its (sqrt(x-2)-1)^2 so you get -2sqrt(x-2)+(x-2)+1=-2sqrt(x-2)+x-1

4. Boxman61 Group Title

hmm ok, my instructors answer is 3...trying to figure it out by your method

5. MCronin Group Title

problem is that you cant square the terms individualy to clear the sqrt

6. Denebel Group Title

Hmm.. it is x^2-14x-33=0

7. MCronin Group Title

doing itnot in my head at 2 am i got x^2-8x+12=0 but still not geting to "3"

8. Boxman61 Group Title

i appreciate the help

9. MCronin Group Title

holy hell dropped the 2 on the right side gimme one sec

10. MCronin Group Title

@denebel has the correct quadratic and it also has one answer that is 3

11. Denebel Group Title

x+5-2*sqrt (x-2) = 2x x+5 = 2x + 2*sqrt (x-2) 5 = 2x + 2*sqrt (x-2) - x 5-x = 2*sqrt (x-2) (5-x)^2 = (2*sqrt (x-2))^2 x^2 - 10x + 25 = 4x - 8 0 = -x^2 + 14x + 33 0 = x^2 - 14x - 33

12. Denebel Group Title

x=3, x=11. Then you check each value by plugging it back into the original equation. Only x=3 checks out, therefore, x=3 is your answer.

13. Denebel Group Title

Oops Typo 0 = -x^2 + 14x - 33 0 = x^2 - 14x + 33

14. Boxman61 Group Title

your awesome, thank you... now to break it down so i learn it lol


text:
# Richard P. Stanley

Richard P. Stanley in Oberwolfach, 1973

Richard Peter Stanley (born June 23, 1944 in New York City ) is an American mathematician and a leading scientist in the field of combinatorics .

## Life

Stanley graduated from Savannah High School in 1962, studied at Caltech (bachelor's degree in 1966) and received his doctorate from Harvard University in 1971 with Gian-Carlo Rota ( Ordered Structures and Partitions. Memoirs of the AMS 1972). At the same time he was a scientist at the Jet Propulsion Laboratory in California from 1965 to 1969 and a teaching assistant at Harvard from 1968 to 1970. In 1970/71 he was a Moore Instructor at the Massachusetts Institute of Technology (MIT) and then until 1973 Miller Research Fellow at the University of California, Berkeley . In 1973 he was an assistant professor at MIT, an associate professor in 1975 and a professor of applied mathematics at MIT in 1979. From 2000 he has been Norman Levinson Professor of Applied Mathematics there. He has held visiting professorships in Stockholm (Mittag-Leffler Institute and Technical University), Augsburg, Japan, Berkeley ( Mathematical Sciences Research Institute , MSRI), Harvard, Strasbourg and San Diego, among others . Since 2003 he has also been a scientist at the Clay Research Academy.

Stanley dealt mainly with combinatorics and their applications, for example in commutative algebra, representation theory and algebraic geometry. He is best known for his work on convex polyhedra (necessity of a condition by Peter McMullen to characterize the -vector of a simplicial polyhedron, which enumerates the number of surfaces according to dimension) and enumerative combinatorics, not least for his textbook. Notorious is an exercise that deals with 66 applications of the Catalan numbers in combinatorics (now expanded to over 160 on his website). ${\ displaystyle f}$

In 1975 he received the Pólya Prize of the Society for Industrial and Applied Mathematics (SIAM), in 2003 the Rolf Schock Prize and in 2001 the Leroy P. Steele Prize (for Enumerative Combinatorics ). In 1983/84 he was a Guggenheim Fellow. He is a member of the National Academy of Sciences (since 1995) and the American Academy of Arts and Sciences (since 1988). In 1983 ( Combinatorial applications of the hard Lefschetz theorem ) and 2006 (plenary lecture: Increasing and Decreasing Subsequences and their Variants ) he was invited speaker at the International Congress of Mathematicians (ICM). He is a fellow of the American Mathematical Society .

In 2007 he worked with Noam Elkies on a book about chess and math.

## Fonts

• Enumerative Combinatorics. 2 vols., 2nd edition Cambridge University Press 1997 (first Wadsworth and Brooks / Cole 1986), ISBN 0-521-55309-1 , ISBN 0-521-56069-1 .
• Combinatorics and commutative algebra. Birkhäuser 1983, 2nd edition 1996
• Hipparch, Plutarch, Schröder and Hough. American Mathematical Monthly, Vol. 104, 1997, p. 344 (on a remark in Plutarch that from 10 elementary over 1 million compound propositions can be formed)
• Patricia Hersh et al. a. (Ed.): Selected works of Richard P. Stanley , AMS 2016

## literature

• Patricia Hersh et al. a .: The mathematical legacy of Richard P. Stanley , AMS 2016

1. Part of the " theorem" suggested by McMullen. Stanley used methods of algebraic geometry (Hartes-Lefschetz theorem, toric varieties) for the proof. Billera and Lee proved the sufficient part of the theorem, also around 1980.${\ displaystyle g}$

format: plain