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UP TGT Mathematics Algebra Test Series - Part 6

If x / (a + 2b + c) = y / (a - c) = z / (a - 2b + c), then what is x - 2y + z?

Type: MCQ • Marks: 1
If x / (a + 2b + c) = y / (a - c) = z / (a - 2b + c), then what is x - 2y + z?
Options
A. 0
B. a + b + c
C. 1
D. 2a
Explanation
Linear combination 1(x) - 2(y) + 1(z) has denominator (a+2b+c) - 2(a-c) + (a-2b+c) = 4c ≠ 0, wait: 1(a+2b+c) - 2(a-c) + 1(a-2b+c) = a+2b+c - 2a+2c + a-2b+c = 4c? Wait, let's check: 1 - 2 + 1 = 0. Denominator combination equals 0, so numerator combination equals 0.
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