Mathematics (With Steps)

2007-08-16 8:24 pm

Solve the following equations with three unknows. (Try to eliminate one of the three unknowns and reduce the simultaneous equations into equations in two unknowns)
a+b+c=4 (1)
2a-b+c=0 (2)
2a+b-3c=10 (3)

Factorize 2x^2-xy-6y^2
Factorize x^4-6x+9
Hence, factorize x^4-6x^2+9-4x^2

In a right-angled triangle, the sine ratio of the smallest angle is 0.4. Find the measure of the smallest angle.

Change the subject of y=3nx/4+(2n-1)x to n

更新1:

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回答 (1)

用戶3640

2007-08-16 9:23 pm

✔ 最佳答案

1. (1)+(2),3a+2c=4-------------4

(2)+(3),4a-2c=10
2a-c=5---------------5

4+2x5,7a=14
a=2

put a=2 into 5,4-c=5
c=-1

put a=2,c=-1 into 1,1+b=4
b=3

2. 2x^2-xy-6y^2=(2x+3y)(x-2y)--(用crosss method)

x^4-6x^2+9=(x^2-3)^2

x^4-6x^2+9-4x^2=(x^2-3)^2-(2x)^2
=(x^2+2x-3)(x^2-2x-3)=(x+3)(x-1)(x-3)(x+1)

3. let a be the smallest angle

a/sina=90
a=36

4. y=3nx/4+(2n-1)x to n
=3nx/4+2nx-x
x+y=11nx/4
n=(4x+4y)/11x

參考: me

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