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Maurinko [17]
3 years ago
10

Identify all of the following solutions of square root of x minus 8 end root plus 8 equals x.

Mathematics
2 answers:
Anit [1.1K]3 years ago
4 0
\sqrt{x-8} +8=x \\  \sqrt{x-8} =x-8 \\  {( \sqrt{x-8} )}^{2} = {(x-8)}^{2}  \\ x-8= x^{2} -16x+64 \\  x^{2} -16x-x+64+8=0 \\  x^{2} -17x+72=0

(x-8)(x-9)=0 \\ x-8=0 \ and \ x-9=0 \\ x=8 \ and \ x=9
9966 [12]3 years ago
3 0

Answer:

Step-by-step explanation:

According to the question, the equation becomes,

\sqrt{x-8}+8=x

⇒\sqrt{x-8}=x-8

Squaring on both the sides, we get

⇒x-8=(x-8)^2

⇒x-8=x^2-16x+64

⇒x^2-16x-x+64+8=0

⇒x^2-17x+72=0

⇒x^2-8x-9x+72=0

⇒x(x-8)-9(x-8)=0

⇒(x-8)(x-9)=0

Then, (x-8)=0

⇒x=8

and (x-9)=0

⇒x=9

Thus, the solution of the given equation is x=8 and x=9.

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