y=sqrt(x+2)to(1)y=√x+2→(1)
(y+x)(y-x)=0larrcolor(blue)"factors of difference of squares"(y+x)(y−x)=0←factors of difference of squares
rArry^2-x^2=0to(2)⇒y2−x2=0→(2)
color(blue)"substitute "y=sqrt(x+2)" into equation "(2)substitute y=√x+2 into equation (2)
(sqrt(x+2))^2-x^2=0(√x+2)2−x2=0
"multiply through by "-1multiply through by −1
x^2-x-2=0larrcolor(blue)"in standard form"x2−x−2=0←in standard form
"the factors of - 2 which sum to - 1 are +1 and - 2"the factors of - 2 which sum to - 1 are +1 and - 2
rArr(x+1)(x-2)=0⇒(x+1)(x−2)=0
"equate each factor to zero and solve for x"equate each factor to zero and solve for x
x+1=0rArrx=-1x+1=0⇒x=−1
x-2=0rArrx=2x−2=0⇒x=2
"substitute these values into equation "(1)substitute these values into equation (1)
x=-1toy=sqrt(-1+2)=1x=−1→y=√−1+2=1
x=2toy=sqrt(2+2)=2x=2→y=√2+2=2
"points of intersection are "(-1,1)" and "(2,2)points of intersection are (−1,1) and (2,2)
