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CBSE Class 12 · 2008 · DeterminantsLong Answer

By using properties of determinants, prove that

a + b + 2 c c c a b + c + 2 a a b b c + a + 2 b = 2 (a + b + c)^{3} .

Answer: Proved

Solution

Apply

C_{1} \to C_{1} + C_{2} + C_{3}

; each entry of column

1

becomes

2 (a + b + c)

. Take it common:

= 2 (a + b + c) 111 a b + c + 2 a a b b c + a + 2 b .

Apply

R_{2} \to R_{2} - R_{1}

,

R_{3} \to R_{3} - R_{1}

to obtain a triangular form with diagonal

(a + b + c)

:

= 2 (a + b + c) \cdot (a + b + c)^{2} = 2 (a + b + c)^{3} .

Proved.

CBSE Class 12 Board · 2008 · Subjective

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