Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 215072 by hardmath last updated on 27/Dec/24

x^2 + 2000x + 1 = 0 Roots: a and b x^2 − 2008x − 1 = 0 Roots: c and d Find: (a+c)(b+d)(a−d)(b−c) = ?

x2+2000x+1=0Roots:aandbx2−2008x−1=0Roots:canddFind:(a+c)(b+d)(a−d)(b−c)=?

Commented by TonyCWX08 last updated on 28/Dec/24

Next time. Have your answer as ANSWER. Not COMMENT.

Nexttime.HaveyouranswerasANSWER.NotCOMMENT.

Commented by Abdullahrussell last updated on 28/Dec/24

(a+c)(b+d)(a−d)(b−c) =(ab+ad+bc+cd)(ab−ac−bd+cd) =(1+ad+bc−1)(1−ac−bd−1) =−(ad+bc)(ac+bd) =−(a^2 cd+abd^2 +abc^2 +b^2 cd) =−(−a^2 +d^2 +c^2 −b^2 ) =a^2 +b^2 −(c^2 +d^2 ) =(a+b)^2 −2ab−(c+d)^2 +2cd =(−2000)^2 −2−(2008)^2 −2 =(2000+2008)(2000−2008)−4 =4008×−8−4 =−32064−4=−32068

(a+c)(b+d)(a−d)(b−c)=(ab+ad+bc+cd)(ab−ac−bd+cd)=(1+ad+bc−1)(1−ac−bd−1)=−(ad+bc)(ac+bd)=−(a2cd+abd2+abc2+b2cd)=−(−a2+d2+c2−b2)=a2+b2−(c2+d2)=(a+b)2−2ab−(c+d)2+2cd=(−2000)2−2−(2008)2−2=(2000+2008)(2000−2008)−4=4008×−8−4=−32064−4=−32068

Commented by MathematicalUser2357 last updated on 28/Dec/24

You better not to be angry

Commented by mr W last updated on 29/Dec/24

i think he is not angry. he is just giving an useful suggestion.

ithinkheisnotangry.heisjustgivinganusefulsuggestion.

Answered by TonyCWX08 last updated on 28/Dec/24

a+b=−2000 ab=1 c+d=2008 cd=−1 (a+c)(b+d) =ab+ad+bc+cd =ad+bc (a−d)(b−c) =ab−ac−bd+cd =−ac−bd (ad+bc)(−ac−bd) =−a^2 cd−abd^2 −ac^2 b−b^2 cd =a^2 −d^2 −c^2 +b^2 =a^2 +b^2 −(c^2 +d^2 ) =((a+b)^2 −2ac)−((c+d)^2 −2cd) =2000^2 −2−(2008^2 +2) =2000^2 −2008^2 −4 =−32068

a+b=−2000ab=1c+d=2008cd=−1(a+c)(b+d)=ab+ad+bc+cd=ad+bc(a−d)(b−c)=ab−ac−bd+cd=−ac−bd(ad+bc)(−ac−bd)=−a2cd−abd2−ac2b−b2cd=a2−d2−c2+b2=a2+b2−(c2+d2)=((a+b)2−2ac)−((c+d)2−2cd)=20002−2−(20082+2)=20002−20082−4=−32068

Terms of Service

Privacy Policy

Contact: info@tinkutara.com