If a^2 + b^2 = 29 and ab = 10, find: (i) a + b (ii) a - b

Question

KnowledgeBoat · Accepted Answer

(i) Using the formula, [∵(x \+ y)² = x² \+ 2xy \+ y²] So, (a \+ b)² = a² \+ 2ab \+ b² Putting the value, a² \+ b² = 29 and ab = 10 ⇒ (a \+ b)² = (a² \+ b²) \+ 2ab ⇒ (a \+ b)² = (29) \+ 2 10 ⇒ (a \+ b)² = 29 \+ 20 ⇒ (a \+ b)² = 49 ⇒ a \+ b = ⇒ a \+ b = 7 or -7 Hence, the values of (a \+ b) are 7 or -7. (ii) Using the formula, [∵(x \- y)² = x² \- 2xy \+ y²] So, (a \- b)² = a² \- 2ab \+ b² Putting the value, a² \+ b² = 29 and ab = 10 ⇒ (a \- b)² = (a² \+ b²) \- 2ab ⇒ (a \- b)² = (29) \- 2 10 ⇒ (a \- b)² = 29 \- 20 ⇒ (a \- b)² = 9 ⇒ a \- b = ⇒ a \- b = 3 or -3 Hence, the values of (a \- b) are 3 or -3.

Mathematics

If a² + b² = 29 and ab = 10, 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

Mathematics

If a2 + b2 = 29 and ab = 10, find:(i) a + b(ii) a - b

Identities

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(i) a + b
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