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(01.03)

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

User Bryan B
by
8.5k points

2 Answers

4 votes

Answer:

= 7

Explanation:

User MikhilMC
by
8.5k points
3 votes

Answer:

x=7 satisfy the equation, so it is the solution.

x=4 doesn't satisfy the equation so it is extraneous solution.

Explanation:

The equation given is:


√(x-3)+5=x

Adding -5 on both sides


√(x-3)=x-5

Taking square on both sides


(√(x-3))^2=(x-5)^2

Now solving


x-3 = x^2 -10x+25\\Arranging\\x^2-10x-x+3+25=0\\x^2-11x+28=0\\Factorizingx^2-7x-4x+28=0\\\\x(x-7)-4(x-7)=0\\(x-4)(x-7)=0\\x-4=0 \,\,and\,\, x-7=0\\x=4 \,\,and\,\, x=7

Verifying solutions:

Putting x=4 in the equation


√(x-3)+5=x


√(4-3)+5=4


√(1)+5=4


1+5=4


6\\eq 4

So, x=4 doesn't satisfy the equation so it is extraneous solution.

Now Putting x=7 and verifying


√(x-3)+5=x


√(7-3)+5=7


√(4)+5=7


2+5=7


7=7

x=7 satisfy the equation, so it is the solution.

User Jweyrich
by
9.2k points

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