Question

Show all work to solve the equation for x. If a solution is extraneous, be sure to identify it in your final answer.

square root of the quantity x minus 3 end quantity plus 5 equals x

Answer 1

Explanation:

Answer 2

Explanation:

`√(x-3) +5=x\\√(x-3) =x-5\\squaring ~both~sides\\x-3=x^2-10x+25\\x^2-10x-x+25+3=0\\x^2-11x+28=0\\x^2-7x-4x+28=0\\x(x-7)-4(x-7)=0\\(x-7)(x-4)=0\\x=7,4`

put x=7 in the given equation

`√(7-3) +5=7\\√(4) +5=7\\2+5=7\\7=7`

which is true .

∴ x=7 is a solution of the given eq.

now put x=4 in the given eq.

`√(4-3) +5=7\\1+5=7\\6=7\\`

which is not true.

∴x=4 is an extraneous solution.