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Question Number 131525 by mathlove last updated on 05/Feb/21
if (a−b)(a+b)=23 then faind a∙b=?
if(a−b)(a+b)=23thenfainda⋅b=?
Answered by mr W last updated on 05/Feb/21
no unique solution for a,b∈R. for a,b∈Z: (a−b)(a+b)=23=1×23 ⇒a−b=1 ⇒a+b=23 ⇒a=((1+23)/2)=12 ⇒b=((23−1)/2)=11 ⇒a×b=12×11=131 or a−b=−1 a+b=−23 ⇒a=−12 ⇒b=−11 ⇒a×b=131
nouniquesolutionfora,b∈R.fora,b∈Z:(a−b)(a+b)=23=1×23⇒a−b=1⇒a+b=23⇒a=1+232=12⇒b=23−12=11⇒a×b=12×11=131ora−b=−1a+b=−23⇒a=−12⇒b=−11⇒a×b=131
Commented by mathlove last updated on 05/Feb/21
thanks
thanks
Commented by Rasheed.Sindhi last updated on 06/Feb/21
Also possible: a+b=1 ∧ a−b=23 a=12,b=−11 a.b=−132 OR a+b=−1 ∧ a−b=−23 a=−12,b=11 a.b=−132
Alsopossible:a+b=1∧a−b=23a=12,b=−11a.b=−132ORa+b=−1∧a−b=−23a=−12,b=11a.b=−132
Commented by mr W last updated on 06/Feb/21
correct sir! thanks for remark!
correctsir!thanksforremark!

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