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Mathematics

(i) If (a + b) = 7 and ab = 10, find the value of (a - b).

(ii) If (x - y) = 5 and xy = 24, find the value of (x + y).

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Answer

(i) Given,

(a + b) = 7 and ab = 10

Using identity,

⇒ (a + b)2 - (a - b)2 = 4ab

Substituting values we get :

⇒ (7)2 - (a - b)2 = 4 × 10

⇒ 49 - (a - b)2 = 40

⇒ (a - b)2 = 49 - 40

⇒ (a - b)2 = 9

⇒ (a - b)2 = 9\sqrt{9}

⇒ (a - b) = ±3\pm 3

Hence, (a - b) = ±3\pm 3.

(ii) Given,

(x - y) = 5 and xy = 24

Using identity,

⇒ (x + y)2 - (x - y)2 = 4xy

⇒ (x + y)2 = 4xy + (x - y)2

⇒ (x + y)2 = 4 × 24 + (5)2

⇒ (x + y)2 = 96 + 25

⇒ (x + y) = 121\sqrt{121}

⇒ (x + y) = ±11\pm 11

Hence, (x + y) = ±11\pm 11.

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