If a^2 + b^2 = 10 and ab = 3, find: (i) a - b (ii) a + b

(i) Using the formula, [∵(x \- y) 2 = x 2 \- 2xy \+ y 2 ] So, (a \- b) 2 = a 2 \- 2ab \+ b 2 Putting the value, a 2 \+ b 2 = 10 and ab = 3 ⇒ (a \- b) 2 = (a 2 \+ b 2 ) \- 2ab ⇒ (a \- b) 2 = (10) \- 2 3 ⇒ (a \- b) 2 = 10 \- 6 ⇒ (a \- b) 2 = 4 ⇒ a \- b = ⇒ a \- b = 2 or -2 Hence, the values of (a \- b) are 2 or -2. (ii) Using the formula, [∵(x \+ y) 2 = x 2 \+ 2xy \+ y 2 ] So, (a \+ b) 2 = a 2 \+ 2ab \+ b 2 Putting the value, a 2 \+ b 2 = 10 and ab = 3 ⇒ (a \+ b) 2 = (a 2 \+ b 2 ) \+ 2ab ⇒ (a \+ b) 2 = (10) \+ 2 3 ⇒ (a \+ b) 2 = 10 \+ 6 ⇒ (a \+ b) 2 = 16 ⇒ a \+ b = ⇒ a \+ b = 4 or -4 Hence, the values of (a \+ b) are 4 or -4.

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Mathematics

If a² + b² = 10 and ab = 3, find:
(i) a - b
(ii) a + b

Identities

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If a² + b² = 10 and ab = 3, find:
(i) a - b
(ii) a + b

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