Question

Calculati, scriind expresia de sub radical sub forma de patrat al unui binom
√3+√8 -√9-2√8-√6+2√8 = ???? + etapele rezolvarii
unde: 3+√8 este sub radical
          9-2√8 este sub radical
          6+2√8 este sub radical

Answer 1

$\sqrt{3+ \sqrt{8} }= \sqrt{3+2 \sqrt{2} } = \sqrt{(1+ \sqrt{2})^2 }= \sqrt{2}+1 \\ \sqrt{9- 2\sqrt{8} }= \sqrt{9-4 \sqrt{2} } = \sqrt{(1-2\sqrt{2})^2 }= 2\sqrt{2}-1 \\ \sqrt{6+ 2\sqrt{8} }= \sqrt{6+4 \sqrt{2} } = \sqrt{(2+ \sqrt{2})^2 }= 2+\sqrt{2} \\ S=-2 \sqrt{2}$

Answer 2

√3+√8
A=3
B=8
C²=A²-B=9-8=1   ⇒C=1
√3+√8=  √3+1/2  +  √3-1/2=    √4/2  + √2/2=  √2+1

√9-2√8= √9-32
A=9
B=32
C²=A²-B=   81-32=49    ⇒C=7
√9-2√8=  √9+7/2-  √9-7/2= √16/2 -√2/2= √8- √1= 2√2-1

√6+2√8=√6-32
A=6
B=32
C²=A²-B=  36-32=4⇒  C=2
√6+2√8= √6+2/2 + √6-2/2=  √8/2  +√4/2=  √4+√2=  2+ √2

S=√2+1-2√2+1-2-2-√2=  -2√2-2=  -2(√2+1)