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Question Number 147500 by mathdanisur last updated on 21/Jul/21

x^2 - y^2 + 2x = 22 what is the number of complete solutions that satisf the equation (x;y).?

x2−y2+2x=22whatisthenumberofcompletesolutionsthatsatisftheequation(x;y).?

Commented by Mrsof last updated on 21/Jul/21

x^2 +2x+1−y^2 =22+1⇒(x+1)^2 −y^2 =23 it is four solution

x2+2x+1−y2=22+1⇒(x+1)2−y2=23itisfoursolution

Answered by Rasheed.Sindhi last updated on 21/Jul/21

I assumed ′number of integer solutions′ x^2 - y^2 + 2x = 22 x^2 +2x+1 - y^2 = 22+1 (x+1)^2 −y^2 =23 (x−y+1)(x+y+1)=23 23=1×23=23×1=−1×−23=−23×−1 ^• x−y+1=1 ∧ x+y+1=23 ^• x−y+1=−1 ∧ x+y+1=−23 ^• x−y+1=23 ∧ x+y+1=1 ^• x−y+1=−23 ∧ x+y+1=−1 Four non-singular systems of simultaneous linear equations. ∴ FOUR integral solutions

Iassumed′numberofintegersolutions′x2−y2+2x=22x2+2x+1−y2=22+1(x+1)2−y2=23(x−y+1)(x+y+1)=2323=1×23=23×1=−1×−23=−23×−1∙x−y+1=1∧x+y+1=23∙x−y+1=−1∧x+y+1=−23∙x−y+1=23∧x+y+1=1∙x−y+1=−23∧x+y+1=−1Fournon−singularsystemsofsimultaneouslinearequations.∴FOURintegralsolutions

Commented by mathdanisur last updated on 21/Jul/21

thank you Sir

thankyouSir

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