Find the value of \(\frac{x}{4}\) if \(2 \sqrt{17 - x} = 2x - 10\).
Answer (2)
\\\\2 \sqrt{17-x} =2(x-5)\ /:2\\\\ \sqrt{17-x} =x-5\ \ \ \Rightarrow\ \ \ (\sqrt{17-x})^2 =(x-5)^2\\\\17-x=x^2-10x+25\\\\"> 2 17 − x = 2 x − 10 ⇒ D : ( 17 − x ≥ 0 an d 2 x − 10 ≥ 0 ) . x ≤ 17 x ≥ 5 . D =< 5 ; 17 > 2 17 − x = 2 ( x − 5 ) / : 2 17 − x = x − 5 ⇒ ( 17 − x ) 2 = ( x − 5 ) 2 17 − x = x 2 − 10 x + 25
x 2 − 9 x + 18 = 0 x 2 − 3 x − 6 x + 18 = 0 x ( x − 3 ) − 6 ( x − 3 ) = 0 ( x − 3 ) ( x − 6 ) = 0 ⇔ ( x − 3 = 0 or x − 6 = 0 ) x = 3 ∈ / D x = 6 ∈ D ⇒ 4 x = 4 6 = 1.5 A n s . 4 x = 1.5
Upon solving the equation 2 17 − x = 2 x − 10 , we find that the only valid solution is x = 8 . Therefore, 4 x = 2 .
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