a) \(\sqrt{x-2}+\sqrt{16x-32}=10\)
\(\Rightarrow\sqrt{x-2}+4\sqrt{x-2}=10\)
\(\Rightarrow5\sqrt{x-2}=10\)
\(\Rightarrow\sqrt{x-2}=2\)
\(\Rightarrow x-2=4\)
\(\Rightarrow x=6\)
b) \(\sqrt{x+\sqrt{2x-1}}=5\sqrt{2}\)
ĐK \(x\ge\dfrac{1}{2}\)
\(\sqrt{x+\sqrt{2x-1}}=5\sqrt{2}\)
\(\left(\sqrt{x+\sqrt{2x-1}}\right)^2=\left(5\sqrt{2}\right)^2\)
\(\left|x+\sqrt{2x-1}\right|=50\)
\(\sqrt{2x-1}=50-x\)
\(\left(\sqrt{2x-1}\right)^2=\left(50-x\right)^2\)
\(\left|2x-1\right|=x^2-100x+2500\)
\(2x-1=x^2-100x+2500\)
\(x=41\)
a) ĐK x\(\ge\)2
\(\sqrt{x-2}+\sqrt{16x-32}=10\)
\(\sqrt{x-2}+\sqrt{16\left(x-2\right)}=10\)
\(\sqrt{x-2}+4\sqrt{x-2}=10\)
\(\left(1+4\right)\sqrt{x-2}=10\)
\(5\sqrt{x-2}=10\)
\(\sqrt{x-2}=2\)
\(\left(\sqrt{x-2}\right)^2=4\)
\(\left|x-2\right|=4\)(vì \(x\ge2\))
\(x-2=4\)
\(x=6\)
b) ĐK: x \(\ge\) 0
\(\sqrt{x+\sqrt{2x-1}}=5\sqrt{2}\)
\(\Rightarrow\sqrt{x+\sqrt{2x-1}}=\sqrt{50}\)
\(\Rightarrow x+\sqrt{2x-1}=50\)
\(\Rightarrow2x-1=2500-100x+x^2\)
\(\Rightarrow102x=2501+x^2\)
\(\Rightarrow x\left(102-x\right)=41.\left(102-41\right)\)
\(\Rightarrow x=41\)
c) ĐK: \(x\ge-1\)
\(x-2\sqrt{x+1}=14\)
\(\Rightarrow\sqrt{4x+4}=x-14\)
\(\Rightarrow4x+4=x^2-28x+196\)
\(\Rightarrow32x=x^2+192\)
\(\Rightarrow x\left(32-x\right)=24\left(32-24\right)\)
\(\Rightarrow x=24\)
c) \(x-2\sqrt{x+1}=14\)
ĐK \(x\ge-1\)
\(x-2\sqrt{x+1}=14\)
\(x-14=2\sqrt{x+1}\)
\(\dfrac{x-14}{2}=\sqrt{x+1}\)
\(\left(\dfrac{x-14}{2}\right)^2=\left(\sqrt{x+1}\right)^2\)
\(\dfrac{\left(x-14\right)^2}{4}=\left|x+1\right|\)
\(x^2-28x+196=4x+x\)
\(x=24\)
