求解=.=
本帖最後由 承b 於 15-12-2011 17:40 編輯1.Let r1 and r2 be the two real roots of the equation (x-2006)(x-2007)=2007. if r is the smaller real root of the equation (x-r1)(x-r2)=-2007,find the value of r.
2.the area of the largest rectangle with perimeter 1 metre is b square metre,find the value of b.
3.x^y+x^-y=(2)2^(1/2) and x^y-x^-y=k,where x>1 and y>0,find the value of k.
4.48^x=2 48^y=3if 8^((x+y)/(1-x-y))=b find the value of b.
5.suppose x^(1/2)+x^(-1/2)=3 and b=(x^(3/2)+x^(-3/2)-3)/(x^2+(x^-2)-2),find the value of b.
唔比用計數機{:14_711:}help= = 1)
What is b?
2)
just form a suitable equation to find the relevant length and width!
3)
http://upload.wikimedia.org/wikipedia/en/math/6/3/7/63781c766e4f6fa778bf2c46022d77c9.png
http://upload.wikimedia.org/wikipedia/en/math/3/9/2/392129ed34619d965cb94cb1bedbc55b.png
Therefore, http://upload.wikimedia.org/wikipedia/en/math/f/1/e/f1e7c7622358307afa7d7db20cf71cdb.png (*)
http://upload.wikimedia.org/wikipedia/en/math/c/6/f/c6f760a5d15f22ffb9d5af317d45c4eb.png
http://upload.wikimedia.org/wikipedia/en/math/0/e/0/0e09613f37e03cdf3a31ef78e383ad16.png
k=2 or -2 from (*)
for x>1 and y>0,
http://upload.wikimedia.org/wikipedia/en/math/9/a/7/9a7999d1fb4a8ff47b3f96ea3d4c398a.png
http://upload.wikimedia.org/wikipedia/en/math/3/8/5/385a0873926bfad4e675c2d5cc72e1d2.png
4)
http://upload.wikimedia.org/wikipedia/en/math/5/a/3/5a3a40901ea74a83a163d5d073b79a18.png
http://upload.wikimedia.org/wikipedia/en/math/5/1/0/510fb4eca5868d0f81a17fd437c08df1.png
considering http://upload.wikimedia.org/wikipedia/en/math/f/3/a/f3abd509816e39741d15cee6bfa94864.png,
therefore http://upload.wikimedia.org/wikipedia/en/math/1/7/4/174427632a5502857e03250c0ec2f167.png
5)
http://upload.wikimedia.org/wikipedia/en/math/9/2/b/92bff65af271be2a6fa2350c52820f82.png
So http://upload.wikimedia.org/wikipedia/en/math/2/4/6/246eb3ee4ac4ae97581b07b74ba61eb9.png (*)
consider http://upload.wikimedia.org/wikipedia/en/math/d/6/7/d67680d33565ebfc714f398ed7d66b25.png,
http://upload.wikimedia.org/wikipedia/en/math/3/d/c/3dc285d56174ac3e97bc19f346e87c8e.png
consider http://upload.wikimedia.org/wikipedia/en/math/d/5/9/d59882e0882997f98156592da742cdbb.png, from (*)
thus http://upload.wikimedia.org/wikipedia/en/math/a/9/4/a94a0d4f3033da6aae50ba8cdaf5b763.png
b=1/3 本帖最後由 承b 於 15-12-2011 17:56 編輯
sorry= =,打錯野,第1題果個r黎,,你好勁,解左幾耐= =
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