Question

If f(x) = `|((1 + x)^17, (1 + x)^19, (1 + x)^23),((1 + x)^23, (1 + x)^29, (1 + x)^34),((1 +x)^41, (1 +x)^43, (1 + x)^47)|` = A + Bx + Cx² + ..., then A = ______.

Answer 1

If f(x) = `|((1 + x)^17, (1 + x)^19, (1 + x)^23),((1 + x)^23, (1 + x)^29, (1 + x)^34),((1 +x)^41, (1 +x)^43, (1 + x)^47)|` = A + Bx + Cx² + ..., then A = 0.

Explanation:

Given that `|((1 + x)^17, (1 + x)^19, (1 + x)^23),((1 + x)^23, (1 + x)^29, (1 + x)^34),((1 +x)^41, (1 +x)^43, (1 + x)^47)|` = A + Bx + Cx² + ...

Taking (1 + x)¹⁷, (1 + x)²³ and (1 + x)⁴¹ common from R₁, R₂ and R₃ respectively

`(1 + x)^17 * (1 + x)^23 * (1 + x)^41 |(1, (1 + x)^2, (1  x)^6),(1, (1 + x)^6, (1 + x)^11),(1, (1 + x)^2, (1 + x)^6)|`

`(1 + x)^17 * (1 + x)^23 * (1 + x)^41 * 0`  ....(R₁ and R₃ are identical)

∴ 0 = A + Bx + Cx² + …

By comparing the like terms, we get A = 0.