y x2 5 y 6x Do two cases y 6x and y 6xSolutiongiven y
{y = x^2 + 5 y = |6x| Do two cases: y = 6x and y = -6x.
Solution
given y = x^2 +5 , y=|6x|
so both equations left handside we have y so we can equal the righthand side also
so x^2 +5 = |6x|
x^2 +5 = 6x when x >0
x^2 -6x +5=0
x^2 -5x-x+5=0
x(x-5)-1(x-5)=0
(x-1)(x-5)=0
so (x-1) =0 or (x-5)=0
(x-1) =0 or (x-5)=0
x=1 or x=5
when x <0
x^2 +5 =-6x
x^2 +6x +5=0
x^2 +5x+x+5=0
x(x+5)+1(x+5)=0
(x+1)(x+5)=0
so (x+1) =0 or (x+5)=0
x=-1 or x=-5
