Cho biết : \(\sqrt{x^2-6x+13}-\sqrt{x^2-6x+10}\)=1
Tính : \(\sqrt{x^2-6x+13}+\sqrt{x^2-6x+10}\)=?
Cho \(\sqrt{x^2-6x+13}-\sqrt{x^2-6x+10}=1\) Tính: \(A=\sqrt{x^2-6x+13}+\sqrt{x^2-6x+10}\)
Ta có: \(A\cdot1=\left(\sqrt{x^2-6x+13}+\sqrt{x^2-6x+10}\right)\left(\sqrt{x^2-6x+13}-\sqrt{x^2-6x+10}\right)=x^2-6x+13-x^2+6x-10=3\)
=> A = 3
Cho biết \(\sqrt{x^2-6x+13}\) - \(\sqrt{x^2-6x+10}\)
Tính \(\sqrt{x^2-6x+13}\) + \(\sqrt{x^2-6x+10}\)
Ta có :
\(\sqrt{x^2-6x+13}-\sqrt{x^2-6x+10}\)
=\(\sqrt{x^2-2.3.x+3^2+4}-\sqrt{x^2-2.3.x+3^2+1}\)
=\(\sqrt{\left(x-3\right)^2+2^2}-\sqrt{\left(x-3\right)^2+1^2}\)
Ta có :
\(\sqrt{x^2-6x+13}+\sqrt{x^2-6x+10}\)
\(=\sqrt{x^2-6x+9+4}+\sqrt{x^2-6x+9+1}\)
\(=\sqrt{\left(x-3\right)^2+2^2}+\sqrt{\left(x-3\right)^2+1}\)
\(Cho\sqrt{x^{ }2-6x+13}-\sqrt{x^{ }2-6x+10}=0\)
Tính \(\sqrt{x^{ }2-6x+13}+\sqrt{x^{ }2-6x+10}\)
cho \(\sqrt{x^2-6x+13}-\sqrt{x^2-6x+10}=1\)
hãy tính \(\sqrt{x^2-6x+13}+\sqrt{x^2-6x+10}\)
(\(\sqrt{x^2-6x+13}\) - \(\sqrt{x^2-6x+10}\))(\(\sqrt{x^2-6x+13}\) + \(\sqrt{x^2-6x+10}\)) = x2 - 6x + 13 - x2 + 6x - 10 = 3
=>
\(\sqrt{x^2-6x+13}\) + \(\sqrt{x^2-6x+10}\) = 3
\(\sqrt{x^2-6x+13}-\sqrt{x^2-6x+10}\)= 1
Tính \(\sqrt{x^2-6x+13}+\sqrt{x^2-6x+10}\)
\(\left(\sqrt{x^2-6x+13}+\sqrt{x^2-6x+10}\right)\left(\sqrt{x^2-6x+13}-\sqrt{x^2-6x+10}\right)=x^2-6x+13-\left(x^2-6x+10\right)\)
\(\Rightarrow\left(\sqrt{x^2-6x+13}+\sqrt{x^2-6x+10}\right).1=3\)
1 Cho a=\(\frac{-1+\sqrt{2}}{2}\)
b=\(\frac{-1-\sqrt{2}}{2}\)
Tính \(a^7+b^7\)
2 Cho biết \(\sqrt{x^2-6x+13}-\sqrt{x^2-6x+10}=1\)
Tính \(\sqrt{x^2-6x+13}+\sqrt{x^2-6x+10}\)
2) Dễ thấy\(\left(\sqrt{x^2-6x+13}-\sqrt{x^2-6x+10}\right)\left(\sqrt{x^2-6x+13}+\sqrt{x^2-6x+10}\right)=x^2-6x+13-x^2+6x-10=3\)
\(\Leftrightarrow1.\left(\sqrt{x^2-6x+13}+\sqrt{x^2-6x+10}\right)=3\)
\(\Leftrightarrow\sqrt{x^2-6x+13}+\sqrt{x^2-6x+10}=3\)
Ta có: a+ b= \(\frac{-1+\sqrt{2}}{2}\) + \(\frac{-1-\sqrt{2}}{2}\)= -1
a*b = \(\frac{-1+\sqrt{2}}{2}\)* \(\frac{-1-\sqrt{2}}{2}\)= -\(\frac{1}{4}\)
a2 + b2 = (a+ b)2 - 2ab = 1+ \(\frac{1}{2}\)= \(\frac{3}{2}\)
a4 + b4 = (a2 + b2 )2 - 2a2b2 = \(\frac{9}{4}\)- \(\frac{1}{8}\)= \(\frac{17}{8}\)
a3 + b3 = ( a + b)3 - 3ab(a + b ) = -1-\(\frac{3}{4}\)= \(\frac{-7}{4}\)
vay a7 + b7 = (a3 + b3 )(a4 + b4 ) -a3b3(a+b)= \(\frac{-7}{4}\)* \(\frac{17}{8}\)- (-\(\frac{1}{64}\)) * (-1) = \(\frac{-239}{64}\)
cho \(\sqrt{x^2-6x+19}\)-\(\sqrt{x^2-6x+10}\)=3 . tính giá trị của T=\(\sqrt{x^2-6x+19}+\sqrt{x^2-6x+10}\)
\(3T=\left(\sqrt{x^2-6x+19}-\sqrt{x^2-6x+10}\right)\left(\sqrt{x^2-6x+19}+\sqrt{x^2-6x+10}\right)\)
\(=x^2-6x+19-\left(x^2-6x+10\right)=9\)
\(\Rightarrow T=3\)
Cho \(\sqrt{x^2-6x+19}-\sqrt{x^2-6x+10}=3\)
Tính M = \(\sqrt{x^2-6x+19}+\sqrt{x^2-6x+10}\)
Giải Phương Trình
a)\(\sqrt{x^2-6x+1}+\sqrt{x^2-6x+13}+\sqrt[4]{x^2-4x+5}=3+\sqrt{2}\)
b)\(\frac{x^2-6x+15}{x^2-6x+11}=\sqrt{x^2-6x+18}\)