Question

if pa = qb = rc and pqr = 1 then prove that , ab + bc + ca = 0​

Answer 1

Answer:

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Class 12

>>Maths

>>Determinants

>>Properties of Determinants

>>If p + q + r = 0 , then pro...

Question

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If p+q+r=0, then prove that

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pa

qc

rb

qb

ra

pc

rc

pb

qa

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=pqr

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a

c

b

b

a

c

c

b

a

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.

Hard

Solution

verified

Verified by Toppr

Given p+q+r=0

∴p

3

+q

3

+r

3

=3pqr

⇒p

3

+q

3

+r

2

−3pqr=0 (i)

R.H.S=pqr

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a

c

b

b

a

c

c

b

a

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Applying C

1

→C

1

+C

2

+C

3

=pqr

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a+b+c

a+b+c

a+b+c

b

a

c

c

b

a

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=pqr(a+b+c)

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1

1

1

b

a

c

c

b

a

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Applying R

2

→R

2

−R

1