Menu Close

if-a-3-b-3-513-ab-54-than-a-b-




Question Number 159394 by azadsir last updated on 16/Nov/21
if a^3 −b^3 =513, ab=54   than, a−b = ?
ifa3b3=513,ab=54than,ab=?
Commented by cortano last updated on 16/Nov/21
a^3 −b^3 =(a−b)(a^2 +b^2 +ab)=513  (a−b)((a−b)^2 +3ab))=513  (a−b)((a−b)^2 +162)=513  x^3 +162x−513=0  (x−3)(x^2 +3x+171)=0   ⇒x=3∈R ; a−b=3
a3b3=(ab)(a2+b2+ab)=513(ab)((ab)2+3ab))=513(ab)((ab)2+162)=513x3+162x513=0(x3)(x2+3x+171)=0x=3R;ab=3
Commented by azadsir last updated on 16/Nov/21
Thank you
Thankyou
Answered by Rasheed.Sindhi last updated on 16/Nov/21
Another Way:  b=((54)/a)  a^3 −(((54)/a))^3 =513  a^6 −513a^3 −54^3 =0  a^3 =((513±(√(513^2 +4.54^3 )))/2)=729,−216  a=9,−6⇒b=((54)/9),((54)/(−6))=6,−9  a−b=9−6, −6−(−9)=3,3  ∴ a−b=3
AnotherWay:b=54aa3(54a)3=513a6513a3543=0a3=513±5132+4.5432=729,216a=9,6b=549,546=6,9ab=96,6(9)=3,3ab=3
Answered by Rasheed.Sindhi last updated on 16/Nov/21
Still Another Way...  ab=54⇒b=((54)/a)  a−((54)/a)=c=?  (a−((54)/a))^3 =c^3   a^3 −((54^3 )/a^3 )−3(a)(((54)/a))(a−((54)/a))=c^3   513−3(a)(((54)/a))(c)=c^3   c^3 +162c−513=0  (c−3)(c^2 +3x+171)=0  c−3=0 ⇒c=3  c=a−b=3
StillAnotherWayab=54b=54aa54a=c=?(a54a)3=c3a3543a33(a)(54a)(a54a)=c35133(a)(54a)(c)=c3c3+162c513=0(c3)(c2+3x+171)=0c3=0c=3c=ab=3

Leave a Reply

Your email address will not be published. Required fields are marked *