Can anyone help?!!!!

2007-10-05 8:04 am
1a. Simplify (√x + √y)(√x - √y)
b. Given that x>y>0, use the result of part (a) to prove that √x > √y.
c. The figure shows a right-angled triangle. If a < 65 and b< 72, find the range of values of the length of the hypotenuse c.

http://i176.photobucket.com/albums/w188/tonywai123/tri.jpg

回答 (3)

2007-10-05 8:36 am
✔ 最佳答案
1a. Simplify (√x + √y)(√x - √y)
(√x + √y)(√x - √y)
= (√x)^2 - (√y)^2
= x - y

b. Given that x>y>0, use the result of part (a) to prove that √x > √y.
(√x + √y)(√x - √y) = x - y > 0
because (√x + √y) > 0,
so √x - √y > 0
√x > √y

c. The figure shows a right-angled triangle. If a < 65 and b< 72, find the range of values of the length of the hypotenuse c
a < 65 , a^2 < 4225
b< 72, b^2 < 5184
a^2 + b^2 < 4225 + 5184 = 9409
a^2 + b^2 < 9409
√(a^2 + b^2) < √9409 = 97
c = √(a^2 + b^2)
c < 97
2007-10-05 8:39 am
1a) 把 √x 當 a, √y當b。即是 (a+b) (a-b) = a2-b2
=  (√x )2 - (√y)2
= x-y

b) Since x&gt;y&gt;0, x-y&gt;0 i.e (√x )2 - (√y)2 &gt;0
(√x )2 &gt; (√y)2
[(√x )2]1/2 &gt; [(√y)2]1/2
√x &gt; √y.

c) don&#39;t know
2007-10-05 8:38 am
a)
(√x + √y)(√x - √y) = (√x)^2 + (√y)^2 = x - y

b)
x&gt;y&gt;0
x-y&gt;0
(√x + √y)(√x - √y) &gt; 0
√x - √y &gt; 0 since (√x + √y) &gt; 0

c)
c^2 = a^2 + b^2
&lt; 65^2 + 72^2 = 97
0&lt;= c &lt; 97


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