Question

Ma puteti ajuta , va rog? :>
9.(u-√2)² - (u+√2)² >√8, u ∈ Z

10.Fie ABC un triunghi, asyfel incat AB=Ac=2 com si BC de x cm , x ∈ N.Ce valori poate lua x?

Answer 1

$(u- \sqrt{2} ) ^{2} - (u+ \sqrt{2}) ^{2} \ \textgreater \ \sqrt{8} \ \textless \ =\ \textgreater \ \\ \ \textless \ =\ \textgreater \ [(u- \sqrt{2})+(u+ \sqrt{2} )][(u- \sqrt{2})-(u+ \sqrt{2})]\ \textgreater \ \sqrt{8} \ \textless \ =\ \textgreater \ \\ \ \textless \ =\ \textgreater \ 2u*(- 2\sqrt{2} )\ \textgreater \ \sqrt{8} \ \textless \ =\ \textgreater \ \\ \ \textless \ =\ \textgreater \ -4u\ \textgreater \ 2=\ \textgreater \ u\ \textless \ - \frac{2}{4}=- \frac{1}{2}$

Deci u∈ (-∞;$- \frac{1}{2}$).
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Intr-un triunghi avem urmatoarele relatii: AB+AC>BC ; AB+BC>AC ; AC+BC>AB ;
|AB-BC|<AC ; |AB-AC|<BC si |BC-AC|<AB.
O vom folosi doar pe prima.

AB+AC>BC <=> 2+2>BC <=> 4>BC.
Dar BC>0, deci 0<BC<4 => BC∈(0;4).