Menu Close

x-2ab-a-b-then-prove-that-x-a-x-a-x-b-x-b-2-




Question Number 185876 by MATHEMATICSAM last updated on 29/Jan/23
x = ((2ab)/(a+b)) then prove that   ((x + a)/(x − a)) + ((x + b)/(x − b)) = 2
x=2aba+bthenprovethatx+axa+x+bxb=2
Answered by Rasheed.Sindhi last updated on 29/Jan/23
x = ((2ab)/(a+b)) then prove that   ((x + a)/(x − a)) + ((x + b)/(x − b)) = 2     LHS:  =((x + a)/(x − a))−1 + ((x + b)/(x − b))−1+2  =((2a)/(x−a))+((2b)/(x−b))+2  =((2a)/(((2ab)/(a+b))−a))+((2b)/(((2ab)/(a+b))−b))+2  =((2a)/((2ab−a^2 −ab)/(a+b)))+((2b)/((2ab−ab−b^2 )/(a+b)))+2  =(2/((b−a)/(a+b)))+(2/((a−b)/(a+b)))+2  =−((2(a+b))/(a−b))+((2(a+b))/(a−b))+2               =2=RHS         Proved
x=2aba+bthenprovethatx+axa+x+bxb=2LHS:=x+axa1+x+bxb1+2=2axa+2bxb+2=2a2aba+ba+2b2aba+bb+2=2a2aba2aba+b+2b2ababb2a+b+2=2baa+b+2aba+b+2=2(a+b)ab+2(a+b)ab+2=2=RHSProved
Answered by ajfour last updated on 29/Jan/23
Assuming true that which to  prove;  (x+a)(x−b)+(x−a)(x+b)          =2(x−a)(x−b)  ⇒ −2ab=−2(a+b)x+2ab  ⇒   x=((2ab)/(a+b))  (so must be)
Assumingtruethatwhichtoprove;(x+a)(xb)+(xa)(x+b)=2(xa)(xb)2ab=2(a+b)x+2abx=2aba+b(somustbe)
Answered by HeferH last updated on 29/Jan/23
 i. x(a +b) = 2ab   ii. ((x + a)/(x −a)) + ((x + b)/(x − b)) = 2 + 2((a/(x − a)) + (b/(x − b)))    = 2 + 2[((a(x−b) + b(x−a))/((x−a)(x−b)))]   = 2 + 2[((x(a+b)−2ab)/((x−a)(x−b)))]    = 2 + 2[(0/((x−a)(x−b)))] = 2 + 2(0) = 2 ✓
i.x(a+b)=2abii.x+axa+x+bxb=2+2(axa+bxb)=2+2[a(xb)+b(xa)(xa)(xb)]=2+2[x(a+b)2ab(xa)(xb)]=2+2[0(xa)(xb)]=2+2(0)=2

Leave a Reply

Your email address will not be published.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