Question and Answers Forum

All Questions      Topic List

Others Questions

Previous in All Question      Next in All Question      

Previous in Others      Next in Others      

Question Number 56775 by zambolly19 last updated on 23/Mar/19

if x,y∍ℜ,show that ∣x+y∣=∣x∣+∣y∣ iff xy≥0

ifx,y∍ℜ,showthat∣x+y∣=∣x∣+∣y∣iffxy⩾0

Commented by maxmathsup by imad last updated on 23/Mar/19

we have ∣x+y∣^2 −(∣x∣+∣y∣)^2 =x^2 +2xy+y^2 −x^2 −2∣xy∣−y^2 =2(xy−∣xy∣) =0 because xy≥0 ⇒∣x+y∣=∣x∣+∣y∣ .

wehave∣x+y∣2−(∣x∣+∣y∣)2=x2+2xy+y2−x2−2∣xy∣−y2=2(xy−∣xy∣)=0becausexy⩾0⇒∣x+y∣=∣x∣+∣y∣.

Terms of Service

Privacy Policy

Contact: info@tinkutara.com