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04/01/2022 1:11 pm
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If 2x - y - z = 3, x + y - 2z = α, 3x + 3y - βz = 3 has infinite solutions, then find the value of α + β - αβ.
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04/01/2022 1:16 pm
Given,
Δ = 0
\(\begin{bmatrix} 2 & -1 & -1 \\[0.3em] 1 & 1 & -2 \\[0.3em] 3 & 3 & -\beta \end{bmatrix}\) = 0
= 2(-β + 6) + 1(-β + 6) – 1(3 - 3) = 0
β = 6
Δ1 = 0
\(\begin{bmatrix} 2 & -1 & -1 \\[0.3em]\alpha & 1 & -2 \\[0.3em] 3 & 3 & -\beta \end{bmatrix}\) = 0
3(-β + 6) + 1(-αβ + 3) – 1(3α - 3) = 0
or α = 1
Therefore, α + β – αβ
= 1 + 6 – 6
= 1
This post was modified 3 years ago by admin