What should be added to 1 + 2x – 3x2 to get x2 – x – 1?

1.	What should be added to 1 + 2x – 3x2 to get x2 – x – 1?
Answer» Let the added algebraic expression may be ‘A say (1 + 2x – 3x²) + A = x² – x – 1 =A =(x² – x – 1) – (1 + 2x – 3x²) = x² – x – 1 – 1 – 2x + 3x² = (x² + 3x²) + ( – x – 2x) +( – 1 – 1) ∴ A = 4x² – 3x – 2 ∴ The required added expression (A) = 4x² – 3x – 2

Answer»

Let the added algebraic expression may be ‘A say

(1 + 2x – 3x²) + A = x² – x – 1

=A =(x² – x – 1) – (1 + 2x – 3x²)

= x² – x – 1 – 1 – 2x + 3x²

= (x² + 3x²) + ( – x – 2x) +( – 1 – 1)

∴ A = 4x² – 3x – 2

∴ The required added expression (A)

= 4x² – 3x – 2

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