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If a,b,c are in AP then prove that, (bc-a²),(ca-b²),(ab-c²) are in AP.

Posted by Lucifer?? Morningstar?? 5 years, 5 months ago

CBSE > Class 10 > Mathematics

3 answers

Lucifer?? Morningstar?? 5 years, 5 months ago

Koi na

0Thank You

Yogita Ingle 5 years, 5 months ago

Given: a, b and c ar in AP
As we know, if a, b and c are in AP then 2b = a + c------ (1)

We have to prove that ( bc - a² ), ( ca - b² ), ( ab - c² ) are in AP.
For this we should prove : 2( ca - b² ) = ( bc - a² )+ ( ab - c² )

Let us consider ( bc - a² )+ ( ab - c² )
= ab + bc - (a²+c²)
= b( a + c ) - [ (a + c)²- 2ac] [ ∵ a²+b² = (a + b)²- 2ab ]
= b(2b) - [ ( 2b )²-2ac] [ ∵ From (1) ]
= 2b²- 4b²+ 2ac
= 2ac - 2b²
= 2(ca - b²)

1Thank You

Anushka ?? 5 years, 5 months ago

Don't know sorry?

1Thank You

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CBSE > Class 10 > Mathematics