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nobillionaireNobley

\(\sqrt{x-8} +8=x \\ \sqrt{x-8} =x-8 \\ {( \sqrt{x-8} )}^{2} = {(x-8)}^{2} \\ x-8= x^{2} -16x+64 \\ x^{2} -16x-x+64+8=0 \\ x^{2} -17x+72=0\)

\((x-8)(x-9)=0 \\ x-8=0 \ and \ x-9=0 \\ x=8 \ and \ x=9\)

boffeemadrid

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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