Question

Va rog ajutati-ma! (ex21)

Answer 1

Răspuns:

a=|-2√5-4|=|-√2²·5 -4 | =|-√20-4|=|-√20 -√16|

Cum -√20< -√16⇒a= |-√20 -√16| <0 ⇒a=|-√20 -√16| =-(-√20 -√16)=√20+√16

b=√(4-2√5)²

√a²=|a|⇒b=√(4-2√5)² = |4-2√5|=|4-√2²·5|=|4-√20|=|√16-√20|

Cum √16<√20⇒|√20 -√16| <0 ⇒|√20 -√16| =-(√20-√16) =-√20+√16

a= √20 +√16 >0

b=-√20 +√16 =√16-√20 <0

Cum a>0 si b<0 ⇒ a>b

b) p1 =3

p2= 5

map = (a ·p1+b·p2)/p1+p2 = $\frac{(\sqrt{20}+\sqrt{16} )*3+(\sqrt{16} -\sqrt{20})*5 }{3+5} =\frac{3\sqrt{20}+12+20-5\sqrt{20} }{8} =\frac{-2\sqrt{20} +32}{8} =\frac{-2*2\sqrt{5} +32}{8} =\frac{-4\sqrt{5} +32}{8} =\frac{-4\sqrt{5} }{8} +\frac{32}{8} =\frac{-\sqrt{5} }{2}+4 =\frac{-\sqrt{5} }{2}+\frac{8}{2}=\frac{-\sqrt{5} +8}{2}$

Explicație pas cu pas: