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in Linear Equations by (53.1k points)
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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)

1 Answer

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Best 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

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