[toán 9] giải phương trình

D

depvazoi

13x−1+9x+1=16x(x≥1)13\sqrt{x-1}+9\sqrt{x+1}=16x (x \ge 1)
<=>16x−13x−1−9x+1=0<=>16x-13\sqrt{x-1}-9\sqrt{x+1}=0
<=>13x−13−13x−1+134+3x+3−9x+1+274=0<=>13x-13-13\sqrt{x-1}+\dfrac{13}{4}+3x+3-9\sqrt{x+1}+\dfrac{27}{4}=0
<=>13(x−1−12)2+3(x+1−32)2=0<=>13(\sqrt{x-1}-\dfrac{1}{2})^2+3(\sqrt{x+1}-\dfrac{3}{2})^2=0
<=>{x−1−12=0x+1−32=0<=> \left\{\begin{matrix} \sqrt{x-1}-\dfrac{1}{2}=0\\\sqrt{x+1}-\dfrac{3}{2}=0 \end{matrix}\right.
<=>x=54(N)<=>x=\dfrac{5}{4} (N)
Vậyx=54Vậy x=\dfrac{5}{4}
 
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