Solution x2 – 5x + 6 = 0 (given)
Appendix 1
PROOFS IN MATHEMATICS
Rationalised 2023-24
 MATHEMATICS
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⇒ (x – 3) (x – 2) = 0 (replacing an expression by an equal/equivalent expression)
⇒ x – 3 = 0 or x – 2 = 0 (from the established theorem ab = 0 ⇒ either a = 0 or
b = 0, for a, b in R)
⇒ x – 3 + 3 = 0 + 3 or  x – 2 + 2 = 0 + 2 (adding equal quantities on either side of the
equation does not alter the nature of the
equation)
⇒ x + 0 = 3 or x + 0 = 2  (using the identity property of integers under addition)
⇒ x = 3 or x = 2 (using the identity property of integers under addition)
Hence, x2 – 5x + 6 = 0 implies x = 3 or x = 2 Explanation Let p be the given statement “x2 – 5x + 6 = 0” and q be the conclusion
statement “x = 3 or x = 2” From the statement p, we deduced the statement r : “(x – 3) (x – 2) = 0” by
replacing the expression x2 – 5x + 6 in the statement p by another expression (x – 3)
(x – 2) which is equal to x2 – 5x + 6 (i)There arise two questions:
How does the expression (x – 3) (x – 2) is equal to the expression x2 – 5x + 6