Solve the simultaneous equations y = √#x#+2 and (#y+x#)(#y-x#)=0 ?
1 Answer
Nov 18, 2017
Explanation:
#y=sqrt(x+2)to(1)#
#(y+x)(y-x)=0larrcolor(blue)"factors of difference of squares"#
#rArry^2-x^2=0to(2)#
#color(blue)"substitute "y=sqrt(x+2)" into equation "(2)#
#(sqrt(x+2))^2-x^2=0#
#"multiply through by "-1#
#x^2-x-2=0larrcolor(blue)"in standard form"#
#"the factors of - 2 which sum to - 1 are +1 and - 2"#
#rArr(x+1)(x-2)=0#
#"equate each factor to zero and solve for x"#
#x+1=0rArrx=-1#
#x-2=0rArrx=2#
#"substitute these values into equation "(1)#
#x=-1toy=sqrt(-1+2)=1#
#x=2toy=sqrt(2+2)=2#
#"points of intersection are "(-1,1)" and "(2,2)#