Math help? (1 Viewer)

[sugarcoated]

These questions are out of the math in focus prelim book page 139


a) Find the value of b in x^2 - 8x + b^2 is a perfect square. hence solve x^2 - 8x - 1 =0 by completing the square.

ans is
b=4;x= ±√17 +14 ≑ 8.12,-0,123

I don't get what im being asked to do, also what does ≑ mean?

b) |3y - 1| + |2y + 3| > 5

ans is
y<-1,Y>3/5


Help me and i'll love you

 

[dan964]

These questions are out of the math in focus prelim book page 139


a) Find the value of b in x^2 - 8x + b^2 is a perfect square. hence solve x^2 - 8x - 1 =0 by completing the square.

ans is
b=4;x= ±√17 +14 ≑ 8.12,-0,123

I don't get what im being asked to do, also what does ≑ mean?

b) |3y - 1| + |2y + 3| > 5

ans is
y<-1,Y>3/5


Help me and i'll love you

The symbol means approximately equal to. Perfect squares factorise to the form (ax+b)^2 (in this case a=1), that should start you off.
Completing the square means you want to find something of the form (x+b)^2 = c


skeleton:
Solve the equation 3y-1 + 2y + 3 = 5 that is 5y = 3
-3y+1 + 2y + 3 = 5 that is -y=1.
(There may be other cases e.g. 3y+1-2y-3=5 and -3y+1-2y-3=5, but these two are enough)
etc.

plot solutions on a number line and test to see if condition holds.