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This is a question of CBSE Sample Paper - Class 12 - 2017/18.

You can download the question paper here  https://www.teachoo.com/cbse/sample-papers/


If Delta = -4, find value of | a^3 - 1 0 a - a^4 0 a-a^4 a^3 - 1

Question 13 - CBSE Class 12 Sample Paper for 2018 Boards - Part 2
Question 13 - CBSE Class 12 Sample Paper for 2018 Boards - Part 3 Question 13 - CBSE Class 12 Sample Paper for 2018 Boards - Part 4

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Transcript

Question 13 If ∆ = |■8(1&𝑎&𝑎2@𝑎&𝑎2&1@𝑎2&1&𝑎)| = −4 Then find the value of |■8(𝑎3−1&0&𝑎−𝑎4@0&𝑎−𝑎4&𝑎3−1@𝑎−𝑎4&𝑎3 −1&0)| Given |■8(1&𝑎&𝑎2@𝑎&𝑎2&1@𝑎2&1&𝑎)| = −4 1 (a2 × a – 1 × 1) – a(a × a – a2 × 1) + a2 (a × 1 – a2 × a2) = – 4 1 (a3 – 1) – a(a2 – a2) + a2 (a – a4) = – 4 (a3 – 1) – a(0) + a2 (a – a4) = – 4 (a3 – 1) + a2 (a – a4) = – 4 (a3 – 1) + a2 × a(1 – a3) = – 4 (a3 – 1) + a3 (1 – a3) = – 4 (a3 – 1) – a3 (a3 – 1) = – 4 (a3 – 1)(1 – a3) = – 4 – (a3 – 1) (a3 – 1) = – 4 (a3 – 1) (a3 – 1) = 4 (a3 – 1)2 = 4 Now, we need to find |■8(𝑎3−1&0&𝑎−𝑎4@0&𝑎−𝑎4&𝑎3−1@𝑎−𝑎4&𝑎3 −1&0)| = (𝑎^3−1)[(𝑎−𝑎^4 )×0−(𝑎^3−1)(𝑎^3−1)] – 0[0×0−(𝑎−𝑎^4 )(𝑎^3−1)] + (𝑎−𝑎^4 )[0×(𝑎^3−1)−(𝑎−𝑎^4 )(𝑎−𝑎^4 )] = (𝑎^3−1)[0−(𝑎^3−1)(𝑎^3−1)] – 0 + (𝑎−𝑎^4 )[0−(𝑎−𝑎^4 )(𝑎−𝑎^4 )] = −(𝑎^3−1)^3−(𝑎−𝑎^4 )^3 = −(𝑎^3−1)^3−〖(𝑎(1−𝑎^3)) 〗^3 = −(𝑎^3−1)^3−〖𝑎^3 (1−𝑎^3)〗^3 = −(𝑎^3−1)^3−〖𝑎^3 ×(−1)^3 (𝑎^3−1)〗^3 = −(𝑎^3−1)^3−〖𝑎^3 ×(−1)^3 (𝑎^3−1)〗^3 = −(𝑎^3−1)^3−〖𝑎^3 ×(−1) × (𝑎^3−1)〗^3 = −(𝑎^3−1)^3+〖𝑎^3 (𝑎^3−1)〗^3 = (𝑎^3−1)^3 (−1+𝑎^3) = (𝑎^3−1)^3 (𝑎^3−1) = (𝑎^3−1)^4 = [(𝑎^3−1)^2 ]^2 Putting (a3 – 1)2 = 4 from (1) = [4]^2 = 16 = −(𝑎^3−1)^3−〖𝑎^3 ×(−1)^3 (𝑎^3−1)〗^3 = −(𝑎^3−1)^3−〖𝑎^3 ×(−1) × (𝑎^3−1)〗^3 = −(𝑎^3−1)^3+〖𝑎^3 (𝑎^3−1)〗^3 = (𝑎^3−1)^3 (−1+𝑎^3) = (𝑎^3−1)^3 (𝑎^3−1) = (𝑎^3−1)^4 = [(𝑎^3−1)^2 ]^2 Putting (a3 – 1)2 = 4 from (1) = [4]^2 = 16

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.