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Question

Using properties of determinants prove that

x+42x2x2xx+42x2x2xx+4=5x+4 4-x2

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Solution

=x+42x2x2xx+42x2x2xx+4=5x+45x+45x+42xx+42x2x2xx+4 Applying R1R1+R2+R3=5x+41112xx+42x2x2xx+4 Take out 5x+4 common from R1=5x+41002x4-x02x04-x Applying C2C2-C1 and C3C3-C1=5x+4(4-x)2 Expanding along R1

Hence proved.

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