Q. 175.0( 3 Votes )

If a, b, c are in A.P. then prove that (a – c)2 = 4 (b2 – ac).

Answer :

Given, a, b and c are in A.P.


We know that when t1, t2, t3 … are in A.P., t3 – t2 = t2 – t1


c – b = b – a


2b = a + c


Squaring on both sides,


(2b)2 = (a + c)2


We know that (a + b)2 = a2 + 2ab + b2.


4b2 = a2 + 2ac + c2


Subtracting 4ac on both sides,


4b2 – 4ac = a2 + 2ac + c2– 4ac


4 (b2 – ac) = a2 – 2ac + c2


4 (b2 – ac) = (a – c)2


Hence proved.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Interactive Quiz:Euclid's Division LemmaInteractive Quiz:Euclid's Division LemmaInteractive Quiz:Euclid's Division Lemma44 mins
Fundamental Theorem of Arithmetic-2Fundamental Theorem of Arithmetic-2Fundamental Theorem of Arithmetic-238 mins
Champ Quiz | Fundamental Principle Of ArithmeticChamp Quiz | Fundamental Principle Of ArithmeticChamp Quiz | Fundamental Principle Of Arithmetic41 mins
Fundamental Theorem of Arithmetic- 1Fundamental Theorem of Arithmetic- 1Fundamental Theorem of Arithmetic- 143 mins
Euclids Division LemmaEuclids Division LemmaEuclids Division Lemma49 mins
Quiz | Imp Qs on Real NumbersQuiz | Imp Qs on Real NumbersQuiz | Imp Qs on Real Numbers37 mins
NCERT | Imp. Qs. on Rational and Irrational NumbersNCERT | Imp. Qs. on Rational and Irrational NumbersNCERT | Imp. Qs. on Rational and Irrational Numbers44 mins
Relation Between LCM , HCF and NumbersRelation Between LCM , HCF and NumbersRelation Between LCM , HCF and Numbers46 mins
Application of Euclids Division LemmaApplication of Euclids Division LemmaApplication of Euclids Division Lemma50 mins
Quiz | Fun with Fundamental Theorem of ArithmeticQuiz | Fun with Fundamental Theorem of ArithmeticQuiz | Fun with Fundamental Theorem of Arithmetic51 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses