Mini HSCs (1 Viewer)

[allGenreGamer]

Here are two questions from the "Mini HSC" which I did in class:

1. 2x + y + (4x - 3y)^(1/2) = 5 +2(6)^(1/2), find x and y. (Sorry, don't have answer)

2. Given cos 2x = 1/5, find the exact value of sin x. (answer = +- (10/5) ^ (1/2) )

I'm totally lost with these two questions, please solve my problems . Thanks.

 

[Xayma]

1.
2x+y=5 ---(1)
4x-3y=24 ---(2) (integer=integer, surd=surd)
From (1)
y=5-2x
Sub y=5-2x in (2)
4x-15+6x=24
10x-15=24
10x=39
x=3.9

Sub x=3.9 in (1)
y=5-2*3.9
y=-2.8

2. If cos 2x=1/5
1-2sin²x=1/5
4/5=2sin²x
2/5=sin² x
sin x=±√ (2/5)

Your answewr is wrong for 2. Even if mine is as well as 10/5 would be simplified to 2.