If a + b = 1 and a - b = 7; find: (i) a2 + b2 (ii) ab

Question

KnowledgeBoat · Accepted Answer

(i) Given: a + b = 1 and a - b = 7 Squaring the given equations, we get: ⇒ (a + b)2 = 12 ⇒ a2 + b2 + 2ab = 1 ...................(1) ⇒ (a - b)2 = 72 ⇒ a2 + b2 - 2ab = 49 ...................(2) Adding equation (1) and (2), ⇒ (a2 + b2 + 2ab) + (a2 + b2 - 2ab) = 1 + 49 ⇒ a2 + b2 + 2ab + a2 + b2 - 2ab = 50 ⇒ 2a2 + 2b2 = 50 ⇒ 2(a2 + b2) = 50 ⇒ a2 + b2 = ⇒ a2 + b2 = 25 Hence, the value of a2 + b2 = 25. (ii) Subtracting equation (2) from equation (1), ⇒ (a2 + b2 + 2ab) - (a2 + b2 - 2ab) = 1 - 49 ⇒ a2 + b2 + 2ab - a2 - b2 + 2ab = -48 ⇒ 4ab = -48 ⇒ ab = = -12 Hence, the value of ab = -12.

Mathematics

If a + b = 1 and a - b = 7; find:
(i) a² + b²
(ii) ab

Expansions

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Mathematics

If a + b = 1 and a - b = 7; find:(i) a2 + b2(ii) ab

Expansions

Related Questions

Expand : (2x - y + 2)3

Expand :(i) (x - 2y + 6)(x - 2y - 6).(ii) (2a - 4b + 7) (2a + 4b + 7).

If x - y + z = 5 and x2 + y2 + z2 = 49, find the value of : zx - xy - yz.

If a + b = 1 and a - b = 7; find:
(i) a² + b²
(ii) ab

Expand : (2x - y + 2)³

Expand :
(i) (x - 2y + 6)(x - 2y - 6).
(ii) (2a - 4b + 7) (2a + 4b + 7).

If x - y + z = 5 and x² + y² + z² = 49, find the value of : zx - xy - yz.