If the sum and the difference of two expressions is 5x2 – x – 4 an

1.	If the sum and the difference of two expressions is 5x2 – x – 4 and x2 + 9x – 10 respectively, then the expressions are : (a) (4x2 + 8x – 6) and (4x2 – 10x + 2)(b) (2x2 + 4x – 3) and (3x2 – 10x – 6) (c) (3x2 + 4x – 7) and (2x2 – 5x + 3) (d) (3x2 + 4x + 7) and (2x2 – 5x – 3)
Answer» (c) (3x² + 4x – 7) and (2x² – 5x + 3 Let the two expressions be A and B. Then, A + B = 5x² – x – 4 .......…(i) A – B = x² + 9x – 10 …(ii) Adding eqn (i) and (ii), we get 2A = (5x² + x² ) + (–x + 9x) + (–4 – 10) = 6x² + 8x –14 \(\Rightarrow\)A = 3x² + 4x – 7 \(\therefore\) From (i), B = (5x² – x – 4) – A = (5x² – x – 4) – (3x² + 4x – 7) = 2x² – 5x + 3

If the sum and the difference of two expressions is 5x2 – x – 4 and x2 + 9x – 10 respectively, then the expressions are : (a) (4x2 + 8x – 6) and (4x2 – 10x + 2)(b) (2x2 + 4x – 3) and (3x2 – 10x – 6) (c) (3x2 + 4x – 7) and (2x2 – 5x + 3) (d) (3x2 + 4x + 7) and (2x2 – 5x – 3)

Answer»

(c) (3x² + 4x – 7) and (2x² – 5x + 3

Let the two expressions be A and B.

Then, A + B = 5x² – x – 4 .......…(i) A – B = x² + 9x – 10 …(ii)

Adding eqn (i) and (ii), we get

2A = (5x² + x² ) + (–x + 9x) + (–4 – 10)

= 6x² + 8x –14

\(\Rightarrow\)A = 3x² + 4x – 7

\(\therefore\) From (i), B = (5x² – x – 4) – A

= (5x² – x – 4) – (3x² + 4x – 7)

= 2x² – 5x + 3