Question

Solve the simultaneous equations y = √`x`+2 and (`y+x`)(`y-x`)=0 ?

Answer 1

`(-1,1),(2,2)`

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`

`>rArrx+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)`