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Mathematics

If a - b = 0.9 and ab = 0.36; find :

(i) a + b

(ii) a2 - b2

Expansions

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Answer

(i) By formula,

⇒ (a + b)2 = (a - b)2 + 4ab

⇒ (a + b)2 = (0.9)2 + 4 × 0.36

⇒ (a + b)2 = 0.81 + 1.44

⇒ (a + b)2 = 2.25

⇒ a + b = 2.25=±1.5\sqrt{2.25} = \pm1.5

Hence, a + b = ±1.5\pm 1.5

(ii) Solving,

⇒ a2 - b2

⇒ (a - b)(a + b)

⇒ 0.9 × ±1.5\pm 1.5

⇒ ±1.35\pm 1.35

Hence, a2 - b2 = ±1.35\pm 1.35

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