Question

\(\dfrac{3}{\sqrt{x}+5}+\dfrac{20-2\sqrt{x}}{x-25}\) .va \(\dfrac{\sqrt{x}+2}{\sqrt{x}+5}\)

tinhs a khi x=9

cho P = \(\dfrac{3.b}{a}\) tim  nguyen de p laf 1 so nguyen

 

Answer 1

a: Khi x=9 thì \(A=\dfrac{3+2}{3+5}=\dfrac{5}{8}\)

b: \(B=\dfrac{3\sqrt{x}-15+20-2\sqrt{x}}{x-25}=\dfrac{\sqrt{x}+5}{x-25}=\dfrac{1}{\sqrt{x}-5}\)

\(P=3\cdot\dfrac{B}{A}=\dfrac{3}{\sqrt{x}-5}\cdot\dfrac{\sqrt{x}+2}{\sqrt{x}+5}=\dfrac{3\sqrt{x}+6}{x-25}\)

Để P là số nguyên thì \(3\sqrt{x}+6⋮x-25\)

=>\(3\left(x-4\right)⋮x-25\)

=>3x-75+63 chia hết cho x-25

=>\(x-25\in\left\{-21;-9;-7;-3;-1;1;3;7;9;21;63\right\}\)

=>\(x\in\left\{4;16;9;22;24;26;28;32;34;46;88\right\}\)