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CBSE Class 12 · 2016 · DeterminantsLong Answer

Using properties of determinants, prove that

(x + y)^{2} z x z y z x (z + y)^{2} x y z y x y (z + x)^{2} = 2 x y z (x + y + z)^{3} .

Answer: Proved

Solution

Multiply

R_{1}, R_{2}, R_{3}

by

z, x, y

respectively and divide by

x y z

, then take

z, x, y

common from

C_{1}, C_{2}, C_{3}

. After

C_{1} \to C_{1} - C_{3}

,

C_{2} \to C_{2} - C_{3}

and taking

(x + y + z)

common from the first two columns, further reduction

R_{3} \to R_{3} - (R_{1} + R_{2})

and expansion give

2 x y z (x + y + z)^{3} .

Proved.

CBSE Class 12 Board · 2016 · Subjective

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